diff --git a/README.md b/README.md index 2cc1f01d1..19ec5824b 100644 --- a/README.md +++ b/README.md @@ -98,6 +98,11 @@ $ conda install -c conda-forge deepxde $ git clone https://github.com/lululxvi/deepxde.git ``` +- If you want to use the new [deepxde.experimental](https://github.com/lululxvi/deepxde/tree/main/deepxde/experimental) module, you can use: +``` sh +$ pip install deepxde[experimental] +``` + ## Explore more - [Install and Setup](https://deepxde.readthedocs.io/en/latest/user/installation.html) diff --git a/docs/experimental_docs/index.rst b/docs/experimental_docs/index.rst new file mode 100644 index 000000000..1d4a545ae --- /dev/null +++ b/docs/experimental_docs/index.rst @@ -0,0 +1,38 @@ +Examples of ``deepxde.experimental`` +==================================== + + +PINN Forward Examples +--------------------- + +.. toctree:: + :maxdepth: 1 + + unit-examples-forward/Beltrami_flow.ipynb + unit-examples-forward/diffusion_1d.ipynb + unit-examples-forward/Euler_beam.ipynb + unit-examples-forward/Helmholtz_Dirichlet_2d.ipynb + unit-examples-forward/burgers.ipynb + unit-examples-forward/Burgers_RAR.ipynb + unit-examples-forward/heat.ipynb + unit-examples-forward/heat_resample.ipynb + unit-examples-forward/Laplace_disk.ipynb + + + +PINN Inverse Examples +--------------------- + +.. toctree:: + :maxdepth: 1 + + unit-examples-inverse/elliptic_inverse_filed.ipynb + unit-examples-inverse/brinkman_forchheimer.ipynb + unit-examples-inverse/diffusion_reaction_rate.ipynb + unit-examples-inverse/reaction_inverse.ipynb + unit-examples-inverse/diffusion_1d_inverse.ipynb + unit-examples-inverse/Navier_Stokes_inverse.ipynb + + + + diff --git a/docs/experimental_docs/unit-examples-forward/Beltrami_flow.ipynb b/docs/experimental_docs/unit-examples-forward/Beltrami_flow.ipynb new file mode 100644 index 000000000..263ddeff7 --- /dev/null +++ b/docs/experimental_docs/unit-examples-forward/Beltrami_flow.ipynb @@ -0,0 +1,591 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "17296f2332f77ca7", + "metadata": {}, + "source": [ + "# Three-dimensional unsteady Navier-Stokes Equations\n", + "\n", + "\n", + "\n", + "## Problem Statement\n", + "\n", + "### 1. Momentum Equations\n", + "\n", + "The Navier-Stokes equations describe the conservation of momentum in fluid dynamics. For an incompressible fluid, the equation is:\n", + "\n", + "$$\n", + "\\frac{\\partial \\mathbf{u}}{\\partial t} + \\mathbf{u} \\cdot \\nabla \\mathbf{u} = - \\nabla p + \\frac{1}{Re} \\nabla^2 \\mathbf{u}\n", + "$$\n", + "\n", + "Where:\n", + "- $\\mathbf{u} = (u, v, w)$ is the velocity field,\n", + "- $p$ is the pressure field,\n", + "- $\\nabla$ is the gradient operator,\n", + "- $\\nabla^2$ is the Laplacian operator,\n", + "- $\\mu$ is the dynamic viscosity.\n", + "\n", + "The momentum equations in the code are written for each of the three spatial components (x, y, z). Specifically, the equations correspond to the following:\n", + "\n", + "\n", + "\n", + "- **$x$-direction momentum equation** (`momentum_x` in the code):\n", + "\n", + "$$\n", + "\\rho\\left[\\frac{\\partial u}{\\partial t}+\\frac{\\partial u}{\\partial x} u+\\frac{\\partial u}{\\partial y} v+\\frac{\\partial u}{\\partial z} w\\right]=-\\frac{\\partial p}{\\partial x}+\\mu\\left(\\frac{\\partial^2 u}{\\partial x^2}+\\frac{\\partial^2 u}{\\partial y^2}+\\frac{\\partial^2 u}{\\partial z^2}\\right)+\\rho g_x\n", + "$$\n", + "\n", + "- **$y$-direction momentum equation** (`momentum_y` in the code):\n", + "\n", + "$$\n", + "\\rho\\left[\\frac{\\partial v}{\\partial t}+\\frac{\\partial v}{\\partial x} u+\\frac{\\partial v}{\\partial y} v+\\frac{\\partial v}{\\partial z} w\\right]=-\\frac{\\partial p}{\\partial y}+\\mu\\left(\\frac{\\partial^2 v}{\\partial x^2}+\\frac{\\partial^2 v}{\\partial y^2}+\\frac{\\partial^2 v}{\\partial z^2}\\right)+\\rho g_y\n", + "$$\n", + "\n", + "- **$z$-direction momentum equation** (`momentum_z` in the code):\n", + "\n", + "$$\n", + "\\rho\\left[\\frac{\\partial w}{\\partial t}+\\frac{\\partial w}{\\partial x} u+\\frac{\\partial w}{\\partial y} v+\\frac{\\partial w}{\\partial z} w\\right]=-\\frac{\\partial p}{\\partial z}+\\mu\\left(\\frac{\\partial^2 w}{\\partial x^2}+\\frac{\\partial^2 w}{\\partial y^2}+\\frac{\\partial^2 w}{\\partial z^2}\\right)+\\rho g_z\n", + "$$\n", + "\n", + "### 2. Continuity Equation\n", + "\n", + "The continuity equation represents the conservation of mass, ensuring that the flow is incompressible (i.e., the divergence of the velocity field is zero). The equation is:\n", + "\n", + "$$\n", + "\\nabla \\cdot \\mathbf{u} = 0\n", + "$$\n", + "\n", + "In the code, the continuity equation corresponds to:\n", + "\n", + "$$\n", + "\\frac{\\partial u}{\\partial x} + \\frac{\\partial v}{\\partial y} + \\frac{\\partial w}{\\partial z} = 0\n", + "$$\n", + "\n", + "This guarantees that the volume of the fluid remains constant and the flow is incompressible.\n", + "\n", + "### 3. Initial and Boundary Conditions (IC and BC)\n", + "\n", + "The function `icbc_cond_func` defines the initial conditions (IC) and boundary conditions (BC) for the velocity and pressure fields.\n", + "\n", + "- **Initial velocity fields**:\n", + " The velocity components are given as functions of spatial variables $x$, $y$, and $z$, as well as time $t$. Specifically, the velocity components $u$, $v$, and $w$ are defined as:\n", + "\n", + "$$\n", + "u = -a \\left( e^{a x} \\sin(a y + d z) + e^{a z} \\cos(a x + d y) \\right) e^{-d^2 t}\n", + "$$\n", + "\n", + "$$\n", + "v = -a \\left( e^{a y} \\sin(a z + d x) + e^{a x} \\cos(a y + d z) \\right) e^{-d^2 t}\n", + "$$\n", + "\n", + "$$\n", + "w = -a \\left( e^{a z} \\sin(a x + d y) + e^{a y} \\cos(a z + d x) \\right) e^{-d^2 t}\n", + "$$\n", + "\n", + "- **Initial pressure field**:\n", + " The pressure field $p$ is given by a more complex expression, involving exponentials and trigonometric functions of the spatial variables $x$, $y$, and $z$:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "p(x, y, z, t)= & -\\frac{1}{2} a^2\\left[e^{2 a x}+e^{2 a y}+e^{2 a z}\\right. \\\\\n", + "& +2 \\sin (a x+d y) \\cos (a z+d x) e^{a(y+z)} \\\\\n", + "& +2 \\sin (a y+d z) \\cos (a x+d y) e^{a(z+x)} \\\\\n", + "& \\left.+2 \\sin (a z+d x) \\cos (a y+d z) e^{a(x+y)}\\right] e^{-2 d^2 t}\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "### 4. Final Formulation: 3D Navier-Stokes Equations\n", + "\n", + "The Navier-Stokes equations, based on the code, are as follows:\n", + "\n", + "#### Momentum Equation (in three dimensions):\n", + "\n", + "$$\n", + "\\frac{\\partial \\mathbf{u}}{\\partial t} + \\mathbf{u} \\cdot \\nabla \\mathbf{u} = - \\nabla p + \\frac{1}{Re} \\nabla^2 \\mathbf{u}\n", + "$$\n", + "\n", + "Where:\n", + "- $\\mathbf{u} = (u, v, w)$ is the velocity field,\n", + "- $p$ is the pressure field,\n", + "- $Re$ is the Reynolds number,\n", + "- $\\nabla^2$ is the Laplacian operator.\n", + "\n", + "#### Continuity Equation (for incompressibility):\n", + "\n", + "$$\n", + "\\nabla \\cdot \\mathbf{u} = 0\n", + "$$\n", + "\n", + "This ensures that the flow remains incompressible.\n", + "\n", + "### Conclusion\n", + "\n", + "The Python code essentially implements the 3D Navier-Stokes equations for an incompressible fluid, where the momentum equations are resolved in each spatial direction, and the continuity equation ensures mass conservation. The initial conditions for velocity and pressure are specified, and boundary conditions are likely handled by the methods in `icbc_cond_func`." + ] + }, + { + "cell_type": "markdown", + "id": "ad99ef67a441b25d", + "metadata": {}, + "source": [ + "## Dimensional Analysis\n", + "\n", + "Summary of Physical Units\n", + "\n", + "- **Velocity ($u, v, w$)**: $[u] = [v] = [w] = \\text{m/s}$\n", + "- **Time ($t$)**: $[t] = \\text{s}$\n", + "- **Pressure ($p$)**: $[p] = \\text{kg/m} \\cdot \\text{s}^2$\n", + "- **Reynolds number ($Re$)**: Dimensionless\n", + "- **Laplacian of velocity ($\\nabla^2 \\mathbf{u}$)**: $\\text{s}^{-2}$\n", + "- **Density ($\\rho$)**: $\\text{kg/m}^3$\n", + "- **Dynamic viscosity ($\\mu$)**: $\\text{kg/m} \\cdot \\text{s}$\n", + "\n", + "The analysis confirms that the Navier-Stokes equations, including the momentum and continuity equations, are dimensionally consistent and properly describe the physical quantities involved in fluid flow.\n" + ] + }, + { + "cell_type": "markdown", + "id": "b2ff0e8c04269c5c", + "metadata": {}, + "source": [ + "## Code Implementation\n", + "\n", + "First, we import the necessary libraries for the implementation:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "9da3a0a3f6e0cfdd", + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T13:35:41.570500Z", + "start_time": "2024-12-17T13:35:39.215212Z" + } + }, + "outputs": [], + "source": [ + "import brainstate as bst\n", + "import brainunit as u\n", + "import jax.tree\n", + "import numpy as np\n", + "\n", + "import deepxde.experimental as deepxde\n" + ] + }, + { + "cell_type": "markdown", + "id": "55d79554e448349a", + "metadata": {}, + "source": [ + "Define the physical units for the problem:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "a7d41ee1906c7370", + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T13:35:41.578528Z", + "start_time": "2024-12-17T13:35:41.574897Z" + } + }, + "outputs": [], + "source": [ + "unit_of_space = u.meter\n", + "unit_of_speed = u.meter / u.second\n", + "unit_of_t = u.second\n", + "unit_of_pressure = u.pascal" + ] + }, + { + "cell_type": "markdown", + "id": "7346e281a5e40f06", + "metadata": {}, + "source": [ + "Define the spatial and temporal domains for the problem:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "c1ebb34b6f25d0a8", + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T13:35:41.632619Z", + "start_time": "2024-12-17T13:35:41.629331Z" + } + }, + "outputs": [], + "source": [ + "spatial_domain = deepxde.geometry.Cuboid(xmin=[-1, -1, -1], xmax=[1, 1, 1])\n", + "temporal_domain = deepxde.geometry.TimeDomain(0, 1)\n", + "spatio_temporal_domain = deepxde.geometry.GeometryXTime(spatial_domain, temporal_domain)\n", + "spatio_temporal_domain = spatio_temporal_domain.to_dict_point(\n", + " x=unit_of_space,\n", + " y=unit_of_space,\n", + " z=unit_of_space,\n", + " t=unit_of_t,\n", + ")\n" + ] + }, + { + "cell_type": "markdown", + "id": "a20e646545ec2cfd", + "metadata": {}, + "source": [ + "Define the neural network model for the problem:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "13fd9b17a2ad3161", + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T13:35:41.978316Z", + "start_time": "2024-12-17T13:35:41.638695Z" + } + }, + "outputs": [], + "source": [ + "net = deepxde.nn.Model(\n", + " deepxde.nn.DictToArray(x=unit_of_space,\n", + " y=unit_of_space,\n", + " z=unit_of_space,\n", + " t=unit_of_t),\n", + " deepxde.nn.FNN([4] + 4 * [50] + [4], \"tanh\", bst.init.KaimingUniform()),\n", + " deepxde.nn.ArrayToDict(u_vel=unit_of_speed,\n", + " v_vel=unit_of_speed,\n", + " w_vel=unit_of_speed,\n", + " p=unit_of_pressure),\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "c49c4dd168704ad2", + "metadata": {}, + "source": [ + "Define the PDE residual function for the Navier-Stokes equations:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "ba050fc459ae4389", + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T13:35:42.026077Z", + "start_time": "2024-12-17T13:35:41.988476Z" + } + }, + "outputs": [], + "source": [ + "\n", + "a = 1\n", + "d = 1\n", + "Re = 1\n", + "rho = 1 * u.kilogram / u.meter ** 3\n", + "mu = 1 * u.pascal * u.second\n", + "\n", + "\n", + "@bst.compile.jit\n", + "def pde(x, u):\n", + " jacobian = net.jacobian(x)\n", + " x_hessian = net.hessian(x, y=['u_vel', 'v_vel', 'w_vel'], xi=['x'], xj=['x'])\n", + " y_hessian = net.hessian(x, y=['u_vel', 'v_vel', 'w_vel'], xi=['y'], xj=['y'])\n", + " z_hessian = net.hessian(x, y=['u_vel', 'v_vel', 'w_vel'], xi=['z'], xj=['z'])\n", + "\n", + " u_vel, v_vel, w_vel, p = u['u_vel'], u['v_vel'], u['w_vel'], u['p']\n", + "\n", + " du_vel_dx = jacobian['u_vel']['x']\n", + " du_vel_dy = jacobian['u_vel']['y']\n", + " du_vel_dz = jacobian['u_vel']['z']\n", + " du_vel_dt = jacobian['u_vel']['t']\n", + " du_vel_dx_dx = x_hessian['u_vel']['x']['x']\n", + " du_vel_dy_dy = y_hessian['u_vel']['y']['y']\n", + " du_vel_dz_dz = z_hessian['u_vel']['z']['z']\n", + "\n", + " dv_vel_dx = jacobian['v_vel']['x']\n", + " dv_vel_dy = jacobian['v_vel']['y']\n", + " dv_vel_dz = jacobian['v_vel']['z']\n", + " dv_vel_dt = jacobian['v_vel']['t']\n", + " dv_vel_dx_dx = x_hessian['v_vel']['x']['x']\n", + " dv_vel_dy_dy = y_hessian['v_vel']['y']['y']\n", + " dv_vel_dz_dz = z_hessian['v_vel']['z']['z']\n", + "\n", + " dw_vel_dx = jacobian['w_vel']['x']\n", + " dw_vel_dy = jacobian['w_vel']['y']\n", + " dw_vel_dz = jacobian['w_vel']['z']\n", + " dw_vel_dt = jacobian['w_vel']['t']\n", + " dw_vel_dx_dx = x_hessian['w_vel']['x']['x']\n", + " dw_vel_dy_dy = y_hessian['w_vel']['y']['y']\n", + " dw_vel_dz_dz = z_hessian['w_vel']['z']['z']\n", + "\n", + " dp_dx = jacobian['p']['x']\n", + " dp_dy = jacobian['p']['y']\n", + " dp_dz = jacobian['p']['z']\n", + "\n", + " momentum_x = (\n", + " rho * (du_vel_dt + (u_vel * du_vel_dx + v_vel * du_vel_dy + w_vel * du_vel_dz))\n", + " + dp_dx - mu * (du_vel_dx_dx + du_vel_dy_dy + du_vel_dz_dz)\n", + " )\n", + " momentum_y = (\n", + " rho * (dv_vel_dt + (u_vel * dv_vel_dx + v_vel * dv_vel_dy + w_vel * dv_vel_dz))\n", + " + dp_dy - mu * (dv_vel_dx_dx + dv_vel_dy_dy + dv_vel_dz_dz)\n", + " )\n", + " momentum_z = (\n", + " rho * (dw_vel_dt + (u_vel * dw_vel_dx + v_vel * dw_vel_dy + w_vel * dw_vel_dz))\n", + " + dp_dz - mu * (dw_vel_dx_dx + dw_vel_dy_dy + dw_vel_dz_dz)\n", + " )\n", + " continuity = du_vel_dx + dv_vel_dy + dw_vel_dz\n", + "\n", + " return [momentum_x, momentum_y, momentum_z, continuity]\n" + ] + }, + { + "cell_type": "markdown", + "id": "7827b37aac032ab8", + "metadata": {}, + "source": [ + "Define the initial and boundary conditions for the problem:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "30611c1e29ef58b8", + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T13:35:42.059708Z", + "start_time": "2024-12-17T13:35:42.050288Z" + } + }, + "outputs": [], + "source": [ + "\n", + "@bst.compile.jit(static_argnums=1)\n", + "def icbc_cond_func(x, include_p: bool = False):\n", + " x = {k: v.mantissa for k, v in x.items()}\n", + "\n", + " u_ = (\n", + " -a\n", + " * (u.math.exp(a * x['x']) * u.math.sin(a * x['y'] + d * x['z'])\n", + " + u.math.exp(a * x['z']) * u.math.cos(a * x['x'] + d * x['y']))\n", + " * u.math.exp(-(d ** 2) * x['t'])\n", + " )\n", + " v = (\n", + " -a\n", + " * (u.math.exp(a * x['y']) * u.math.sin(a * x['z'] + d * x['x'])\n", + " + u.math.exp(a * x['x']) * u.math.cos(a * x['y'] + d * x['z']))\n", + " * u.math.exp(-(d ** 2) * x['t'])\n", + " )\n", + " w = (\n", + " -a\n", + " * (u.math.exp(a * x['z']) * u.math.sin(a * x['x'] + d * x['y'])\n", + " + u.math.exp(a * x['y']) * u.math.cos(a * x['z'] + d * x['x']))\n", + " * u.math.exp(-(d ** 2) * x['t'])\n", + " )\n", + " p = (\n", + " -0.5\n", + " * a ** 2\n", + " * (\n", + " u.math.exp(2 * a * x['x'])\n", + " + u.math.exp(2 * a * x['y'])\n", + " + u.math.exp(2 * a * x['z'])\n", + " + 2\n", + " * u.math.sin(a * x['x'] + d * x['y'])\n", + " * u.math.cos(a * x['z'] + d * x['x'])\n", + " * u.math.exp(a * (x['y'] + x['z']))\n", + " + 2\n", + " * u.math.sin(a * x['y'] + d * x['z'])\n", + " * u.math.cos(a * x['x'] + d * x['y'])\n", + " * u.math.exp(a * (x['z'] + x['x']))\n", + " + 2\n", + " * u.math.sin(a * x['z'] + d * x['x'])\n", + " * u.math.cos(a * x['y'] + d * x['z'])\n", + " * u.math.exp(a * (x['x'] + x['y']))\n", + " )\n", + " * u.math.exp(-2 * d ** 2 * x['t'])\n", + " )\n", + "\n", + " r = {'u_vel': u_ * unit_of_speed,\n", + " 'v_vel': v * unit_of_speed,\n", + " 'w_vel': w * unit_of_speed}\n", + " if include_p:\n", + " r['p'] = p * unit_of_pressure\n", + " return r\n", + "\n", + "\n", + "bc = deepxde.icbc.DirichletBC(icbc_cond_func)\n", + "ic = deepxde.icbc.IC(icbc_cond_func)" + ] + }, + { + "cell_type": "markdown", + "id": "d5663ac4d9b3ae59", + "metadata": {}, + "source": [ + "Define the problem as a TimePDE object:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "3f1612bbaeb56010", + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T13:35:43.072978Z", + "start_time": "2024-12-17T13:35:42.121586Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Warning: 283 points required, but 343 points sampled.\n", + "Warning: 10000 points required, but 12348 points sampled.\n" + ] + } + ], + "source": [ + "problem = deepxde.problem.TimePDE(\n", + " spatio_temporal_domain,\n", + " pde,\n", + " [bc, ic],\n", + " net,\n", + " num_domain=50000,\n", + " num_boundary=5000,\n", + " num_initial=5000,\n", + " num_test=10000,\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "f472396f52fcb8a5", + "metadata": {}, + "source": [ + "Train the model using the problem data:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "71f97c909111b8e1", + "metadata": { + "ExecuteTime": { + "start_time": "2024-12-17T13:35:43.085506Z" + }, + "jupyter": { + "is_executing": true + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Compiling trainer...\n", + "'compile' took 0.051972 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "0 [12.974215 * (kilogram / klitre * (meter / second) / second) ** 2, [14.700201 * (kilogram / klitre * (meter / second) / second) ** 2, [] \n", + " 24.321922 * (kilogram / klitre * (meter / second) / second) ** 2, 29.931065 * (kilogram / klitre * (meter / second) / second) ** 2, \n", + " 13.350433 * (kilogram / klitre * (meter / second) / second) ** 2, 17.096483 * (kilogram / klitre * (meter / second) / second) ** 2, \n", + " 1.2527013 * becquerel2, 1.3801537 * becquerel2, \n", + " {'ibc0': {'u_vel': 2.5884202 * meter / second, {'ibc0': {'u_vel': 2.5884202 * meter / second, \n", + " 'v_vel': 1.5904388 * meter / second, 'v_vel': 1.5904388 * meter / second, \n", + " 'w_vel': 1.7298671 * meter / second}}, 'w_vel': 1.7298671 * meter / second}}, \n", + " {'ibc1': {'u_vel': 4.1043954 * meter / second, {'ibc1': {'u_vel': 4.1043954 * meter / second, \n", + " 'v_vel': 2.08325 * meter / second, 'v_vel': 2.08325 * meter / second, \n", + " 'w_vel': 2.6199307 * meter / second}}] 'w_vel': 2.6199307 * meter / second}}] \n" + ] + } + ], + "source": [ + "model = deepxde.Trainer(problem)\n", + "\n", + "model.compile(bst.optim.Adam(1e-3)).train(iterations=30000)\n", + "model.compile(bst.optim.LBFGS(1e-3)).train(5000, display_every=200)" + ] + }, + { + "cell_type": "markdown", + "id": "becbb0f8333344e9", + "metadata": {}, + "source": [ + "Verify the results by plotting the loss history and the predicted solution:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ca417f07847d6081", + "metadata": {}, + "outputs": [], + "source": [ + "x, y, z = np.meshgrid(np.linspace(-1, 1, 10), np.linspace(-1, 1, 10), np.linspace(-1, 1, 10))\n", + "t_0 = np.zeros(1000)\n", + "t_1 = np.ones(1000)\n", + "X_0 = dict(\n", + " x=np.ravel(x) * unit_of_space,\n", + " y=np.ravel(y) * unit_of_space,\n", + " z=np.ravel(z) * unit_of_space,\n", + " t=t_0 * unit_of_t\n", + ")\n", + "X_1 = dict(\n", + " x=np.ravel(x) * unit_of_space,\n", + " y=np.ravel(y) * unit_of_space,\n", + " z=np.ravel(z) * unit_of_space,\n", + " t=t_1 * unit_of_t\n", + ")\n", + "output_0 = model.predict(X_0)\n", + "output_1 = model.predict(X_1)\n", + "\n", + "out_exact_0 = icbc_cond_func(X_0, True)\n", + "out_exact_1 = icbc_cond_func(X_1, True)\n", + "\n", + "f_0 = pde(X_0, output_0)\n", + "f_1 = pde(X_1, output_1)\n", + "residual_0 = jax.tree.map(lambda x: np.mean(np.absolute(x)), f_0)\n", + "residual_1 = jax.tree.map(lambda x: np.mean(np.absolute(x)), f_1)\n", + "\n", + "print(\"Accuracy at t = 0:\")\n", + "print(\"Mean residual:\", residual_0)\n", + "print(\"L2 relative error:\", deepxde.metrics.l2_relative_error(output_0, out_exact_0))\n", + "print(\"\\n\")\n", + "print(\"Accuracy at t = 1:\")\n", + "print(\"Mean residual:\", residual_1)\n", + "print(\"L2 relative error:\", deepxde.metrics.l2_relative_error(output_1, out_exact_1))\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/experimental_docs/unit-examples-forward/Beltrami_flow.py b/docs/experimental_docs/unit-examples-forward/Beltrami_flow.py new file mode 100644 index 000000000..a90f90d64 --- /dev/null +++ b/docs/experimental_docs/unit-examples-forward/Beltrami_flow.py @@ -0,0 +1,202 @@ +import brainstate as bst +import brainunit as u +import jax.tree +import numpy as np + +import deepxde.experimental as deepxde + +unit_of_space = u.meter +unit_of_speed = u.meter / u.second +unit_of_t = u.second +unit_of_pressure = u.pascal + +spatial_domain = deepxde.geometry.Cuboid(xmin=[-1, -1, -1], xmax=[1, 1, 1]) +temporal_domain = deepxde.geometry.TimeDomain(0, 1) +spatio_temporal_domain = deepxde.geometry.GeometryXTime(spatial_domain, temporal_domain) +spatio_temporal_domain = spatio_temporal_domain.to_dict_point( + x=unit_of_space, + y=unit_of_space, + z=unit_of_space, + t=unit_of_t, +) + +net = deepxde.nn.Model( + deepxde.nn.DictToArray(x=unit_of_space, + y=unit_of_space, + z=unit_of_space, + t=unit_of_t), + deepxde.nn.FNN([4] + 4 * [50] + [4], "tanh", bst.init.KaimingUniform()), + deepxde.nn.ArrayToDict(u_vel=unit_of_speed, + v_vel=unit_of_speed, + w_vel=unit_of_speed, + p=unit_of_pressure), +) + +a = 1 +d = 1 +Re = 1 +rho = 1 * u.kilogram / u.meter ** 3 +mu = 1 * u.pascal * u.second + + +@bst.compile.jit +def pde(x, u): + jacobian = net.jacobian(x) + x_hessian = net.hessian(x, y=['u_vel', 'v_vel', 'w_vel'], xi=['x'], xj=['x']) + y_hessian = net.hessian(x, y=['u_vel', 'v_vel', 'w_vel'], xi=['y'], xj=['y']) + z_hessian = net.hessian(x, y=['u_vel', 'v_vel', 'w_vel'], xi=['z'], xj=['z']) + + u_vel, v_vel, w_vel, p = u['u_vel'], u['v_vel'], u['w_vel'], u['p'] + + du_vel_dx = jacobian['u_vel']['x'] + du_vel_dy = jacobian['u_vel']['y'] + du_vel_dz = jacobian['u_vel']['z'] + du_vel_dt = jacobian['u_vel']['t'] + du_vel_dx_dx = x_hessian['u_vel']['x']['x'] + du_vel_dy_dy = y_hessian['u_vel']['y']['y'] + du_vel_dz_dz = z_hessian['u_vel']['z']['z'] + + dv_vel_dx = jacobian['v_vel']['x'] + dv_vel_dy = jacobian['v_vel']['y'] + dv_vel_dz = jacobian['v_vel']['z'] + dv_vel_dt = jacobian['v_vel']['t'] + dv_vel_dx_dx = x_hessian['v_vel']['x']['x'] + dv_vel_dy_dy = y_hessian['v_vel']['y']['y'] + dv_vel_dz_dz = z_hessian['v_vel']['z']['z'] + + dw_vel_dx = jacobian['w_vel']['x'] + dw_vel_dy = jacobian['w_vel']['y'] + dw_vel_dz = jacobian['w_vel']['z'] + dw_vel_dt = jacobian['w_vel']['t'] + dw_vel_dx_dx = x_hessian['w_vel']['x']['x'] + dw_vel_dy_dy = y_hessian['w_vel']['y']['y'] + dw_vel_dz_dz = z_hessian['w_vel']['z']['z'] + + dp_dx = jacobian['p']['x'] + dp_dy = jacobian['p']['y'] + dp_dz = jacobian['p']['z'] + + momentum_x = ( + rho * (du_vel_dt + (u_vel * du_vel_dx + v_vel * du_vel_dy + w_vel * du_vel_dz)) + + dp_dx - mu * (du_vel_dx_dx + du_vel_dy_dy + du_vel_dz_dz) + ) + momentum_y = ( + rho * (dv_vel_dt + (u_vel * dv_vel_dx + v_vel * dv_vel_dy + w_vel * dv_vel_dz)) + + dp_dy - mu * (dv_vel_dx_dx + dv_vel_dy_dy + dv_vel_dz_dz) + ) + momentum_z = ( + rho * (dw_vel_dt + (u_vel * dw_vel_dx + v_vel * dw_vel_dy + w_vel * dw_vel_dz)) + + dp_dz - mu * (dw_vel_dx_dx + dw_vel_dy_dy + dw_vel_dz_dz) + ) + continuity = du_vel_dx + dv_vel_dy + dw_vel_dz + + return [momentum_x, momentum_y, momentum_z, continuity] + + +@bst.compile.jit(static_argnums=1) +def icbc_cond_func(x, include_p: bool = False): + x = {k: v.mantissa for k, v in x.items()} + + u_ = ( + -a + * (u.math.exp(a * x['x']) * u.math.sin(a * x['y'] + d * x['z']) + + u.math.exp(a * x['z']) * u.math.cos(a * x['x'] + d * x['y'])) + * u.math.exp(-(d ** 2) * x['t']) + ) + v = ( + -a + * (u.math.exp(a * x['y']) * u.math.sin(a * x['z'] + d * x['x']) + + u.math.exp(a * x['x']) * u.math.cos(a * x['y'] + d * x['z'])) + * u.math.exp(-(d ** 2) * x['t']) + ) + w = ( + -a + * (u.math.exp(a * x['z']) * u.math.sin(a * x['x'] + d * x['y']) + + u.math.exp(a * x['y']) * u.math.cos(a * x['z'] + d * x['x'])) + * u.math.exp(-(d ** 2) * x['t']) + ) + p = ( + -0.5 + * a ** 2 + * ( + u.math.exp(2 * a * x['x']) + + u.math.exp(2 * a * x['y']) + + u.math.exp(2 * a * x['z']) + + 2 + * u.math.sin(a * x['x'] + d * x['y']) + * u.math.cos(a * x['z'] + d * x['x']) + * u.math.exp(a * (x['y'] + x['z'])) + + 2 + * u.math.sin(a * x['y'] + d * x['z']) + * u.math.cos(a * x['x'] + d * x['y']) + * u.math.exp(a * (x['z'] + x['x'])) + + 2 + * u.math.sin(a * x['z'] + d * x['x']) + * u.math.cos(a * x['y'] + d * x['z']) + * u.math.exp(a * (x['x'] + x['y'])) + ) + * u.math.exp(-2 * d ** 2 * x['t']) + ) + + r = { + 'u_vel': u_ * unit_of_speed, + 'v_vel': v * unit_of_speed, + 'w_vel': w * unit_of_speed + } + if include_p: + r['p'] = p * unit_of_pressure + return r + + +bc = deepxde.icbc.DirichletBC(icbc_cond_func) +ic = deepxde.icbc.IC(icbc_cond_func) + +problem = deepxde.problem.TimePDE( + spatio_temporal_domain, + pde, + [bc, ic], + net, + num_domain=50000, + num_boundary=5000, + num_initial=5000, + num_test=10000, +) + +model = deepxde.Trainer(problem) + +model.compile(bst.optim.Adam(1e-3)).train(iterations=30000) +model.compile(bst.optim.LBFGS(1e-3)).train(5000, display_every=200) + +x, y, z = np.meshgrid(np.linspace(-1, 1, 10), np.linspace(-1, 1, 10), np.linspace(-1, 1, 10)) +t_0 = np.zeros(1000) +t_1 = np.ones(1000) +X_0 = dict( + x=np.ravel(x) * unit_of_space, + y=np.ravel(y) * unit_of_space, + z=np.ravel(z) * unit_of_space, + t=t_0 * unit_of_t +) +X_1 = dict( + x=np.ravel(x) * unit_of_space, + y=np.ravel(y) * unit_of_space, + z=np.ravel(z) * unit_of_space, + t=t_1 * unit_of_t +) +output_0 = model.predict(X_0) +output_1 = model.predict(X_1) + +out_exact_0 = icbc_cond_func(X_0, True) +out_exact_1 = icbc_cond_func(X_1, True) + +f_0 = pde(X_0, output_0) +f_1 = pde(X_1, output_1) +residual_0 = jax.tree.map(lambda x: np.mean(np.absolute(x)), f_0) +residual_1 = jax.tree.map(lambda x: np.mean(np.absolute(x)), f_1) + +print("Accuracy at t = 0:") +print("Mean residual:", residual_0) +print("L2 relative error:", deepxde.metrics.l2_relative_error(output_0, out_exact_0)) +print("\n") +print("Accuracy at t = 1:") +print("Mean residual:", residual_1) +print("L2 relative error:", deepxde.metrics.l2_relative_error(output_1, out_exact_1)) diff --git a/docs/experimental_docs/unit-examples-forward/Burgers.py b/docs/experimental_docs/unit-examples-forward/Burgers.py new file mode 100644 index 000000000..af7633aaf --- /dev/null +++ b/docs/experimental_docs/unit-examples-forward/Burgers.py @@ -0,0 +1,68 @@ +import brainstate as bst +import brainunit as u +import numpy as np + +import deepxde.experimental as deepxde + +geometry = deepxde.geometry.GeometryXTime( + geometry=deepxde.geometry.Interval(-1, 1.), + timedomain=deepxde.geometry.TimeDomain(0, 0.99) +).to_dict_point(x=u.meter, t=u.second) + +uy = u.meter / u.second +bc = deepxde.icbc.DirichletBC(lambda x: {'y': 0. * uy}) +ic = deepxde.icbc.IC(lambda x: {'y': -u.math.sin(u.math.pi * x['x'] / u.meter) * uy}) + +v = 0.01 / u.math.pi * u.meter ** 2 / u.second + + +def pde(x, y): + jacobian = approximator.jacobian(x) + hessian = approximator.hessian(x) + dy_x = jacobian['y']['x'] + dy_t = jacobian['y']['t'] + dy_xx = hessian['y']['x']['x'] + residual = dy_t + y['y'] * dy_x - v * dy_xx + return residual + + +approximator = deepxde.nn.Model( + deepxde.nn.DictToArray(x=u.meter, t=u.second), + deepxde.nn.FNN( + [geometry.dim] + [20] * 3 + [1], + "tanh", + bst.init.KaimingUniform() + ), + deepxde.nn.ArrayToDict(y=uy) +) + +problem = deepxde.problem.TimePDE( + geometry, + pde, + [bc, ic], + approximator, + num_domain=2540, + num_boundary=80, + num_initial=160, +) + +trainer = deepxde.Trainer(problem) +trainer.compile(bst.optim.Adam(1e-3)).train(iterations=15000) +trainer.compile(bst.optim.LBFGS(1e-3)).train(2000, display_every=500) +trainer.saveplot(issave=True, isplot=True) + + +def gen_testdata(): + data = np.load("../dataset/Burgers.npz") + t, x, exact = data["t"], data["x"], data["usol"].T + xx, tt = np.meshgrid(x, t) + X = {'x': np.ravel(xx) * u.meter, 't': np.ravel(tt) * u.second} + y = exact.flatten()[:, None] + return X, y * uy + + +X, y_true = gen_testdata() +y_pred = trainer.predict(X) +f = pde(X, y_pred) +print("Mean residual:", u.math.mean(u.math.absolute(f))) +print("L2 relative error:", deepxde.metrics.l2_relative_error(y_true, y_pred['y'])) diff --git a/docs/experimental_docs/unit-examples-forward/Burgers_RAR.ipynb b/docs/experimental_docs/unit-examples-forward/Burgers_RAR.ipynb new file mode 100644 index 000000000..160f8ff73 --- /dev/null +++ b/docs/experimental_docs/unit-examples-forward/Burgers_RAR.ipynb @@ -0,0 +1,1424 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Burgers equation with residual-based adaptive refinement\n", + "\n", + "\n", + "## Problem setup\n", + "\n", + "\n", + "We will solve a Burgers equation:\n", + "\n", + "$$\n", + "\\frac{\\partial u}{\\partial t} + u\\frac{\\partial u}{\\partial x} = \\nu\\frac{\\partial^2u}{\\partial x^2}, \\qquad x \\in [-1, 1], \\quad t \\in [0, 1]\n", + "$$\n", + "\n", + "\n", + "with the Dirichlet boundary conditions and initial conditions\n", + "\n", + "$$\n", + "u(-1,t)=u(1,t)=0, \\quad u(x,0) = - \\sin(\\pi x).\n", + "$$\n", + "\n", + "## Dimensional Analysis\n", + "\n", + "### Step 1: Assign Dimensions to Variables\n", + "\n", + "1. **Spatial Coordinate $x$:**\n", + " - The dimension of $x$ is length:\n", + "\n", + " $$\n", + " [x] = L.\n", + " $$\n", + "\n", + "2. **Time $t$:**\n", + " - The dimension of time is:\n", + "\n", + " $$\n", + " [t] = T.\n", + " $$\n", + "\n", + "3. **Velocity $u$:**\n", + " - Velocity has dimensions of length per unit time:\n", + "\n", + " $$\n", + " [u] = L / T.\n", + " $$\n", + "\n", + "4. **Viscosity $\\nu$:**\n", + " - The term $\\nu \\frac{\\partial^2 u}{\\partial x^2}$ involves the second spatial derivative of velocity, which must have the same dimensions as the time derivative $\\frac{\\partial u}{\\partial t}$.\n", + "\n", + "---\n", + "\n", + "### Step 2: Analyze the Dimensions of Each Term\n", + "\n", + "1. **Time Derivative Term:**\n", + " - The time derivative $\\frac{\\partial u}{\\partial t}$ has dimensions:\n", + "\n", + " $$\n", + " \\left[\\frac{\\partial u}{\\partial t}\\right] = \\frac{[u]}{[t]} = \\frac{L / T}{T} = \\frac{L}{T^2}.\n", + " $$\n", + "\n", + "2. **Advection Term:**\n", + " - The advection term $u \\frac{\\partial u}{\\partial x}$ involves the spatial derivative of velocity:\n", + "\n", + " $$\n", + " \\left[u \\frac{\\partial u}{\\partial x}\\right] = [u] \\cdot \\frac{[u]}{[x]} = \\frac{L}{T} \\cdot \\frac{L / T}{L} = \\frac{L}{T^2}.\n", + " $$\n", + "\n", + "3. **Diffusion Term:**\n", + " - The diffusion term $\\nu \\frac{\\partial^2 u}{\\partial x^2}$ involves the second spatial derivative of velocity:\n", + "\n", + " $$\n", + " \\left[\\frac{\\partial^2 u}{\\partial x^2}\\right] = \\frac{[u]}{[x]^2} = \\frac{L / T}{L^2} = \\frac{1}{L T}.\n", + " \n", + " $$\n", + " - Therefore, the diffusion term has dimensions:\n", + "\n", + " $$\n", + " \\left[\\nu \\frac{\\partial^2 u}{\\partial x^2}\\right] = [\\nu] \\cdot \\frac{1}{L T} = \\frac{L}{T^2}.\n", + " $$\n", + "\n", + "---\n", + "\n", + "### Step 3: Determine the Dimensions of $\\nu$\n", + "\n", + "- The diffusion term $\\nu \\frac{\\partial^2 u}{\\partial x^2}$ must have the same dimensions as the time derivative $\\frac{\\partial u}{\\partial t}$:\n", + "\n", + " $$\n", + " [\\nu] \\cdot \\frac{1}{L T} = \\frac{L}{T^2} \\implies [\\nu] = \\frac{L^2}{T}.\n", + " $$\n", + "- Therefore, the viscosity $\\nu$ has dimensions of kinematic viscosity:\n", + "\n", + " $$\n", + " [\\nu] = \\frac{L^2}{T}.\n", + " $$\n", + "\n", + "---\n", + "\n", + "### Step 4: Summary of Dimensions\n", + "\n", + "| Variable/Parameter | Physical Meaning | Dimensions |\n", + "|------------------------|-----------------------------------|-----------------------|\n", + "| $x$ | Spatial coordinate | $L$ |\n", + "| $t$ | Time | $T$ |\n", + "| $u$ | Velocity | $L / T$ |\n", + "| $\\nu$ | Kinematic viscosity | $L^2 / T$ |\n", + "\n", + "---\n", + "\n", + "### Step 5: Initial and Boundary Conditions\n", + "\n", + "1. **Boundary Conditions:**\n", + " - The boundary conditions $u(-1,t) = u(1,t) = 0$ are given in meters per second:\n", + "\n", + " $$\n", + " [u(-1,t)] = [u(1,t)] = L / T.\n", + " $$\n", + "\n", + "2. **Initial Condition:**\n", + " - The initial condition $u(x,0) = -\\sin(\\pi x)$ is given in meters per second:\n", + " \n", + " $$\n", + " [u(x,0)] = L / T.\n", + " $$\n", + " - The term $\\sin(\\pi x)$ is dimensionless because $x$ is in meters, and $\\pi$ is a dimensionless constant." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Implementation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This description goes through the implementation of a solver for the above described Burgers equation step-by-step.\n", + "\n", + "First, import the libraries we need:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "import brainstate as bst\n", + "import brainunit as u\n", + "import numpy as np\n", + "import jax\n", + "import deepxde.experimental as deepxde" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We begin by defining a computational geometry and time domain. We can use a built-in class ``Interval`` and ``TimeDomain`` and we combine both the domains using ``GeometryXTime`` as follows:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "geomtime = deepxde.geometry.GeometryXTime(\n", + " geometry=deepxde.geometry.Interval(-1., 1.),\n", + " timedomain=deepxde.geometry.TimeDomain(0., 0.99)\n", + ").to_dict_point(x=u.meter, t=u.second)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we express the PDE residual of the Burgers equation:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "v = 0.01 / u.math.pi * u.meter ** 2 / u.second\n", + "\n", + "\n", + "def pde(x, y):\n", + " jacobian = approximator.jacobian(x)\n", + " hessian = approximator.hessian(x)\n", + " dy_x = jacobian['y']['x']\n", + " dy_t = jacobian['y']['t']\n", + " dy_xx = hessian['y']['x']['x']\n", + " residual = dy_t + y['y'] * dy_x - v * dy_xx\n", + " return residual" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we consider the boundary/initial condition. ``on_boundary`` is chosen here to use the whole boundary of the computational domain in considered as the boundary condition. We include the ``geomtime`` space, time geometry created above and ``on_boundary`` as the BCs in the ``DirichletBC`` function of DeepXDE. We also define ``IC`` which is the inital condition for the burgers equation and we use the computational domain, initial function, and ``on_initial`` to specify the IC.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "uy = u.meter / u.second\n", + "\n", + "bc = deepxde.icbc.DirichletBC(lambda x: {'y': 0. * uy})\n", + "ic = deepxde.icbc.IC(lambda x: {'y': -u.math.sin(u.math.pi * x['x'] / u.meter) * uy})\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we choose the network. Here, we use a fully connected neural network of depth 4 (i.e., 3 hidden layers) and width 20:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "approximator = deepxde.nn.Model(\n", + " deepxde.nn.DictToArray(x=u.meter, t=u.second),\n", + " deepxde.nn.FNN(\n", + " [geometry.dim] + [20] * 3 + [1],\n", + " \"tanh\",\n", + " bst.init.KaimingUniform()\n", + " ),\n", + " deepxde.nn.ArrayToDict(y=uy)\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, we have specified the geometry, PDE residual, and boundary/initial condition. We then define the ``TimePDE`` problem as\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "problem = deepxde.problem.TimePDE(\n", + " geometry,\n", + " pde,\n", + " [bc, ic],\n", + " approximator,\n", + " num_domain=2540,\n", + " num_boundary=80,\n", + " num_initial=160,\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The number 2540 is the number of training residual points sampled inside the domain, and the number 80 is the number of training points sampled on the boundary. We also include 160 initial residual points for the initial conditions.\n", + "\n", + "Now, we have the PDE problem and the network. We build a ``Trainer`` and choose the optimizer and learning rate:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Compiling trainer...\n", + "'compile' took 0.003058 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "0 [2.1140547 * 10.0^0 * ((meter / second) / second) ** 2, [2.1140547 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 0.09046214 * meter / second}}, {'ibc0': {'y': 0.09046214 * meter / second}}, \n", + " {'ibc1': {'y': 0.23645507 * meter / second}}] {'ibc1': {'y': 0.23645507 * meter / second}}] \n", + "1000 [0.05101593 * 10.0^0 * ((meter / second) / second) ** 2, [0.05101593 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 0.00244636 * meter / second}}, {'ibc0': {'y': 0.00244636 * meter / second}}, \n", + " {'ibc1': {'y': 0.06664469 * meter / second}}] {'ibc1': {'y': 0.06664469 * meter / second}}] \n", + "2000 [0.04578441 * 10.0^0 * ((meter / second) / second) ** 2, [0.04578441 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 0.00104335 * meter / second}}, {'ibc0': {'y': 0.00104335 * meter / second}}, \n", + " {'ibc1': {'y': 0.05536607 * meter / second}}] {'ibc1': {'y': 0.05536607 * meter / second}}] \n", + "3000 [0.04083971 * 10.0^0 * ((meter / second) / second) ** 2, [0.04083971 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 0.00048144 * meter / second}}, {'ibc0': {'y': 0.00048144 * meter / second}}, \n", + " {'ibc1': {'y': 0.05146844 * meter / second}}] {'ibc1': {'y': 0.05146844 * meter / second}}] \n", + "4000 [0.03656165 * 10.0^0 * ((meter / second) / second) ** 2, [0.03656165 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 0.00020483 * meter / second}}, {'ibc0': {'y': 0.00020483 * meter / second}}, \n", + " {'ibc1': {'y': 0.04795899 * meter / second}}] {'ibc1': {'y': 0.04795899 * meter / second}}] \n", + "5000 [0.03201985 * 10.0^0 * ((meter / second) / second) ** 2, [0.03201985 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 5.5738237e-05 * meter / second}}, {'ibc0': {'y': 5.5738237e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.04417896 * meter / second}}] {'ibc1': {'y': 0.04417896 * meter / second}}] \n", + "6000 [0.01897248 * 10.0^0 * ((meter / second) / second) ** 2, [0.01897248 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 3.411638e-05 * meter / second}}, {'ibc0': {'y': 3.411638e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.02110803 * meter / second}}] {'ibc1': {'y': 0.02110803 * meter / second}}] \n", + "7000 [0.0083445 * 10.0^0 * ((meter / second) / second) ** 2, [0.0083445 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.9857232e-05 * meter / second}}, {'ibc0': {'y': 1.9857232e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.00840012 * meter / second}}] {'ibc1': {'y': 0.00840012 * meter / second}}] \n", + "8000 [0.00405152 * 10.0^0 * ((meter / second) / second) ** 2, [0.00405152 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 3.13869e-05 * meter / second}}, {'ibc0': {'y': 3.13869e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.0031565 * meter / second}}] {'ibc1': {'y': 0.0031565 * meter / second}}] \n", + "9000 [0.00258377 * 10.0^0 * ((meter / second) / second) ** 2, [0.00258377 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.9788125e-05 * meter / second}}, {'ibc0': {'y': 2.9788125e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.00185996 * meter / second}}] {'ibc1': {'y': 0.00185996 * meter / second}}] \n", + "10000 [0.00182265 * 10.0^0 * ((meter / second) / second) ** 2, [0.00182265 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.8763618e-05 * meter / second}}, {'ibc0': {'y': 1.8763618e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.00121202 * meter / second}}] {'ibc1': {'y': 0.00121202 * meter / second}}] \n", + "11000 [0.00131502 * 10.0^0 * ((meter / second) / second) ** 2, [0.00131502 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1222968e-05 * meter / second}}, {'ibc0': {'y': 1.1222968e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.00087704 * meter / second}}] {'ibc1': {'y': 0.00087704 * meter / second}}] \n", + "12000 [0.00102354 * 10.0^0 * ((meter / second) / second) ** 2, [0.00102354 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 7.5733656e-06 * meter / second}}, {'ibc0': {'y': 7.5733656e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00069363 * meter / second}}] {'ibc1': {'y': 0.00069363 * meter / second}}] \n", + "13000 [0.00085795 * 10.0^0 * ((meter / second) / second) ** 2, [0.00085795 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 6.1193127e-06 * meter / second}}, {'ibc0': {'y': 6.1193127e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00059203 * meter / second}}] {'ibc1': {'y': 0.00059203 * meter / second}}] \n", + "14000 [0.00075481 * 10.0^0 * ((meter / second) / second) ** 2, [0.00075481 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 5.336154e-06 * meter / second}}, {'ibc0': {'y': 5.336154e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00052162 * meter / second}}] {'ibc1': {'y': 0.00052162 * meter / second}}] \n", + "15000 [0.00067973 * 10.0^0 * ((meter / second) / second) ** 2, [0.00067973 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.3045325e-06 * meter / second}}, {'ibc0': {'y': 4.3045325e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00046943 * meter / second}}] {'ibc1': {'y': 0.00046943 * meter / second}}] \n", + "\n", + "Best trainer at step 15000:\n", + " train loss: 1.15e-03\n", + " test loss: 1.15e-03\n", + " test metric: []\n", + "\n", + "'train' took 60.923828 s\n", + "\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trainer = deepxde.Trainer(problem)\n", + "trainer.compile(bst.optim.Adam(1e-3)).train(iterations=15000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After we train the network using Adam, we continue to train the network using L-BFGS to achieve a smaller loss:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Compiling trainer...\n", + "'compile' took 0.023359 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "15000 [0.00067973 * 10.0^0 * ((meter / second) / second) ** 2, [0.00067973 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.3045325e-06 * meter / second}}, {'ibc0': {'y': 4.3045325e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00046943 * meter / second}}] {'ibc1': {'y': 0.00046943 * meter / second}}] \n", + "15200 [0.00068126 * 10.0^0 * ((meter / second) / second) ** 2, [0.00068126 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.169301e-06 * meter / second}}, {'ibc0': {'y': 4.169301e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00046952 * meter / second}}] {'ibc1': {'y': 0.00046952 * meter / second}}] \n", + "15400 [0.00068003 * 10.0^0 * ((meter / second) / second) ** 2, [0.00068003 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.1923004e-06 * meter / second}}, {'ibc0': {'y': 4.1923004e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00046954 * meter / second}}] {'ibc1': {'y': 0.00046954 * meter / second}}] \n", + "15600 [0.00067914 * 10.0^0 * ((meter / second) / second) ** 2, [0.00067914 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.2128318e-06 * meter / second}}, {'ibc0': {'y': 4.2128318e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00046957 * meter / second}}] {'ibc1': {'y': 0.00046957 * meter / second}}] \n", + "15800 [0.00067831 * 10.0^0 * ((meter / second) / second) ** 2, [0.00067831 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.2393303e-06 * meter / second}}, {'ibc0': {'y': 4.2393303e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0004696 * meter / second}}] {'ibc1': {'y': 0.0004696 * meter / second}}] \n", + "16000 [0.00067745 * 10.0^0 * ((meter / second) / second) ** 2, [0.00067745 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.397528e-06 * meter / second}}, {'ibc0': {'y': 4.397528e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0004696 * meter / second}}] {'ibc1': {'y': 0.0004696 * meter / second}}] \n", + "16200 [0.00067771 * 10.0^0 * ((meter / second) / second) ** 2, [0.00067771 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.1383482e-06 * meter / second}}, {'ibc0': {'y': 4.1383482e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00046968 * meter / second}}] {'ibc1': {'y': 0.00046968 * meter / second}}] \n", + "16400 [0.00067749 * 10.0^0 * ((meter / second) / second) ** 2, [0.00067749 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.25508e-06 * meter / second}}, {'ibc0': {'y': 4.25508e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00046969 * meter / second}}] {'ibc1': {'y': 0.00046969 * meter / second}}] \n", + "16600 [0.00067738 * 10.0^0 * ((meter / second) / second) ** 2, [0.00067738 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.3410837e-06 * meter / second}}, {'ibc0': {'y': 4.3410837e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00046968 * meter / second}}] {'ibc1': {'y': 0.00046968 * meter / second}}] \n", + "16800 [0.0006782 * 10.0^0 * ((meter / second) / second) ** 2, [0.0006782 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 3.657258e-06 * meter / second}}, {'ibc0': {'y': 3.657258e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00047006 * meter / second}}] {'ibc1': {'y': 0.00047006 * meter / second}}] \n", + "17000 [0.00067788 * 10.0^0 * ((meter / second) / second) ** 2, [0.00067788 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 3.8210997e-06 * meter / second}}, {'ibc0': {'y': 3.8210997e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00046992 * meter / second}}] {'ibc1': {'y': 0.00046992 * meter / second}}] \n", + "\n", + "Best trainer at step 16600:\n", + " train loss: 1.15e-03\n", + " test loss: 1.15e-03\n", + " test metric: []\n", + "\n", + "'train' took 9.051486 s\n", + "\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trainer.compile(bst.optim.LBFGS(1e-3)).train(2000, display_every=200)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because we only use 2500 residual points for training, the accuracy is low. Next, we improve the accuracy by the residual-based adaptive refinement (RAR) method. Because the Burgers equation has a sharp front, intuitively, we should put more points near the sharp front. First, we randomly generate 100000 points from our domain to calculate the PDE residual." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "X = geomtime.random_points(100000)\n", + "err = 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will repeatedly add points while the mean residual is greater than 0.005. Each iteration, we use our model to generate predictions for inputs in `X` and compute the absolute values of the errors. We then print the mean residual. Next, we find the points where the residual is greatest and add these new points for training PDE loss. Furthermore, we define a callback function to check whether the network converges. If there is significant improvement in the model’s accuracy, as judged by the callback function, we continue to train the model. As before, after we train the network using Adam, we continue to train the network using L-BFGS to achieve a smaller loss:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean residual: 0.018 * (meter / second) / second\n", + "Adding new point: {'t': ArrayImpl([0.31030682], dtype=float32) * second, 'x': ArrayImpl([0.00072277], dtype=float32) * meter} \n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.013387 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "17000 [0.00295319 * 10.0^0 * ((meter / second) / second) ** 2, [0.00067788 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 3.8210997e-06 * meter / second}}, {'ibc0': {'y': 3.8210997e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00046992 * meter / second}}] {'ibc1': {'y': 0.00046992 * meter / second}}] \n", + "18000 [0.00108327 * 10.0^0 * ((meter / second) / second) ** 2, [0.0009432 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 5.890686e-06 * meter / second}}, {'ibc0': {'y': 5.890686e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00053691 * meter / second}}] {'ibc1': {'y': 0.00053691 * meter / second}}] \n", + "19000 [0.00092558 * 10.0^0 * ((meter / second) / second) ** 2, [0.000839 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.3144605e-06 * meter / second}}, {'ibc0': {'y': 4.3144605e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00054824 * meter / second}}] {'ibc1': {'y': 0.00054824 * meter / second}}] \n", + "20000 [0.00081564 * 10.0^0 * ((meter / second) / second) ** 2, [0.00076047 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 3.5706555e-06 * meter / second}}, {'ibc0': {'y': 3.5706555e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00053703 * meter / second}}] {'ibc1': {'y': 0.00053703 * meter / second}}] \n", + "21000 [0.00096415 * 10.0^0 * ((meter / second) / second) ** 2, [0.00090121 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.095076e-06 * meter / second}}, {'ibc0': {'y': 4.095076e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00050534 * meter / second}}] {'ibc1': {'y': 0.00050534 * meter / second}}] \n", + "22000 [0.00064556 * 10.0^0 * ((meter / second) / second) ** 2, [0.00062304 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 3.185172e-06 * meter / second}}, {'ibc0': {'y': 3.185172e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00046558 * meter / second}}] {'ibc1': {'y': 0.00046558 * meter / second}}] \n", + "23000 [0.00058509 * 10.0^0 * ((meter / second) / second) ** 2, [0.00056849 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 3.078764e-06 * meter / second}}, {'ibc0': {'y': 3.078764e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00042695 * meter / second}}] {'ibc1': {'y': 0.00042695 * meter / second}}] \n", + "24000 [0.00053798 * 10.0^0 * ((meter / second) / second) ** 2, [0.00052545 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.944127e-06 * meter / second}}, {'ibc0': {'y': 2.944127e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0003891 * meter / second}}] {'ibc1': {'y': 0.0003891 * meter / second}}] \n", + "25000 [0.00053603 * 10.0^0 * ((meter / second) / second) ** 2, [0.00052135 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 3.57443e-06 * meter / second}}, {'ibc0': {'y': 3.57443e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00035367 * meter / second}}] {'ibc1': {'y': 0.00035367 * meter / second}}] \n", + "26000 [0.00046754 * 10.0^0 * ((meter / second) / second) ** 2, [0.00046 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.5451907e-06 * meter / second}}, {'ibc0': {'y': 2.5451907e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00032271 * meter / second}}] {'ibc1': {'y': 0.00032271 * meter / second}}] \n", + "27000 [0.00044109 * 10.0^0 * ((meter / second) / second) ** 2, [0.00043435 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.2023457e-06 * meter / second}}, {'ibc0': {'y': 2.2023457e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029436 * meter / second}}] {'ibc1': {'y': 0.00029436 * meter / second}}] \n", + "\n", + "Best trainer at step 27000:\n", + " train loss: 7.38e-04\n", + " test loss: 7.31e-04\n", + " test metric: []\n", + "\n", + "'train' took 38.123230 s\n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.009922 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "27000 [0.00044109 * 10.0^0 * ((meter / second) / second) ** 2, [0.00043435 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.2023457e-06 * meter / second}}, {'ibc0': {'y': 2.2023457e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029436 * meter / second}}] {'ibc1': {'y': 0.00029436 * meter / second}}] \n", + "27100 [0.00044241 * 10.0^0 * ((meter / second) / second) ** 2, [0.00043749 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.3348348e-06 * meter / second}}, {'ibc0': {'y': 2.3348348e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029449 * meter / second}}] {'ibc1': {'y': 0.00029449 * meter / second}}] \n", + "27200 [0.00044184 * 10.0^0 * ((meter / second) / second) ** 2, [0.00043681 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.326817e-06 * meter / second}}, {'ibc0': {'y': 2.326817e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029447 * meter / second}}] {'ibc1': {'y': 0.00029447 * meter / second}}] \n", + "27300 [0.00044135 * 10.0^0 * ((meter / second) / second) ** 2, [0.00043622 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.3192913e-06 * meter / second}}, {'ibc0': {'y': 2.3192913e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029445 * meter / second}}] {'ibc1': {'y': 0.00029445 * meter / second}}] \n", + "27400 [0.00044094 * 10.0^0 * ((meter / second) / second) ** 2, [0.00043571 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.3149416e-06 * meter / second}}, {'ibc0': {'y': 2.3149416e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029443 * meter / second}}] {'ibc1': {'y': 0.00029443 * meter / second}}] \n", + "27500 [0.00044026 * 10.0^0 * ((meter / second) / second) ** 2, [0.00043484 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.307417e-06 * meter / second}}, {'ibc0': {'y': 2.307417e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029437 * meter / second}}] {'ibc1': {'y': 0.00029437 * meter / second}}] \n", + "27600 [0.0004401 * 10.0^0 * ((meter / second) / second) ** 2, [0.00043462 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.3055607e-06 * meter / second}}, {'ibc0': {'y': 2.3055607e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029435 * meter / second}}] {'ibc1': {'y': 0.00029435 * meter / second}}] \n", + "27700 [0.00044003 * 10.0^0 * ((meter / second) / second) ** 2, [0.00043452 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.3062646e-06 * meter / second}}, {'ibc0': {'y': 2.3062646e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029433 * meter / second}}] {'ibc1': {'y': 0.00029433 * meter / second}}] \n", + "27800 [0.00043955 * 10.0^0 * ((meter / second) / second) ** 2, [0.00043361 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.3343398e-06 * meter / second}}, {'ibc0': {'y': 2.3343398e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029413 * meter / second}}] {'ibc1': {'y': 0.00029413 * meter / second}}] \n", + "27900 [0.00043953 * 10.0^0 * ((meter / second) / second) ** 2, [0.00043358 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.3186947e-06 * meter / second}}, {'ibc0': {'y': 2.3186947e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029415 * meter / second}}] {'ibc1': {'y': 0.00029415 * meter / second}}] \n", + "28000 [0.00070291 * 10.0^0 * ((meter / second) / second) ** 2, [0.00070311 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.3909661e-05 * meter / second}}, {'ibc0': {'y': 1.3909661e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.00030785 * meter / second}}] {'ibc1': {'y': 0.00030785 * meter / second}}] \n", + "\n", + "Best trainer at step 27900:\n", + " train loss: 7.36e-04\n", + " test loss: 7.30e-04\n", + " test metric: []\n", + "\n", + "'train' took 4.621998 s\n", + "\n", + "Mean residual: 0.016 * (meter / second) / second\n", + "Adding new point: {'t': ArrayImpl([0.98801452], dtype=float32) * second, 'x': ArrayImpl([-0.00032282], dtype=float32) * meter} \n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.013920 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "28000 [0.00197229 * 10.0^0 * ((meter / second) / second) ** 2, [0.00070311 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.3909661e-05 * meter / second}}, {'ibc0': {'y': 1.3909661e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.00030785 * meter / second}}] {'ibc1': {'y': 0.00030785 * meter / second}}] \n", + "29000 [0.00051649 * 10.0^0 * ((meter / second) / second) ** 2, [0.00050734 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.4825522e-06 * meter / second}}, {'ibc0': {'y': 2.4825522e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0002885 * meter / second}}] {'ibc1': {'y': 0.0002885 * meter / second}}] \n", + "30000 [0.00048944 * 10.0^0 * ((meter / second) / second) ** 2, [0.00048262 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.2519919e-06 * meter / second}}, {'ibc0': {'y': 2.2519919e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00028214 * meter / second}}] {'ibc1': {'y': 0.00028214 * meter / second}}] \n", + "31000 [0.00046857 * 10.0^0 * ((meter / second) / second) ** 2, [0.00046308 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.1248854e-06 * meter / second}}, {'ibc0': {'y': 2.1248854e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0002748 * meter / second}}] {'ibc1': {'y': 0.0002748 * meter / second}}] \n", + "Epoch 31000: early stopping\n", + "\n", + "Best trainer at step 31000:\n", + " train loss: 7.45e-04\n", + " test loss: 7.40e-04\n", + " test metric: []\n", + "\n", + "'train' took 12.569310 s\n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.009631 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "31000 [0.00046857 * 10.0^0 * ((meter / second) / second) ** 2, [0.00046308 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.1248854e-06 * meter / second}}, {'ibc0': {'y': 2.1248854e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0002748 * meter / second}}] {'ibc1': {'y': 0.0002748 * meter / second}}] \n", + "31100 [0.00046857 * 10.0^0 * ((meter / second) / second) ** 2, [0.00046308 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.1262192e-06 * meter / second}}, {'ibc0': {'y': 2.1262192e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0002748 * meter / second}}] {'ibc1': {'y': 0.0002748 * meter / second}}] \n", + "31200 [0.00046849 * 10.0^0 * ((meter / second) / second) ** 2, [0.00046293 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.1473877e-06 * meter / second}}, {'ibc0': {'y': 2.1473877e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027483 * meter / second}}] {'ibc1': {'y': 0.00027483 * meter / second}}] \n", + "31300 [0.00073493 * 10.0^0 * ((meter / second) / second) ** 2, [0.0007051 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 6.5290965e-06 * meter / second}}, {'ibc0': {'y': 6.5290965e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029808 * meter / second}}] {'ibc1': {'y': 0.00029808 * meter / second}}] \n", + "31400 [0.00068256 * 10.0^0 * ((meter / second) / second) ** 2, [0.00065663 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 5.5905107e-06 * meter / second}}, {'ibc0': {'y': 5.5905107e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029581 * meter / second}}] {'ibc1': {'y': 0.00029581 * meter / second}}] \n", + "31500 [0.00063919 * 10.0^0 * ((meter / second) / second) ** 2, [0.00061659 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.833671e-06 * meter / second}}, {'ibc0': {'y': 4.833671e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029365 * meter / second}}] {'ibc1': {'y': 0.00029365 * meter / second}}] \n", + "31600 [0.00060404 * 10.0^0 * ((meter / second) / second) ** 2, [0.00058418 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.2318925e-06 * meter / second}}, {'ibc0': {'y': 4.2318925e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029175 * meter / second}}] {'ibc1': {'y': 0.00029175 * meter / second}}] \n", + "31700 [0.0005764 * 10.0^0 * ((meter / second) / second) ** 2, [0.00055869 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 3.7593527e-06 * meter / second}}, {'ibc0': {'y': 3.7593527e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029007 * meter / second}}] {'ibc1': {'y': 0.00029007 * meter / second}}] \n", + "31800 [0.00055442 * 10.0^0 * ((meter / second) / second) ** 2, [0.00053848 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 3.3909535e-06 * meter / second}}, {'ibc0': {'y': 3.3909535e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00028856 * meter / second}}] {'ibc1': {'y': 0.00028856 * meter / second}}] \n", + "31900 [0.00053654 * 10.0^0 * ((meter / second) / second) ** 2, [0.00052207 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 3.0938609e-06 * meter / second}}, {'ibc0': {'y': 3.0938609e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00028721 * meter / second}}] {'ibc1': {'y': 0.00028721 * meter / second}}] \n", + "32000 [0.00052238 * 10.0^0 * ((meter / second) / second) ** 2, [0.00050915 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.8530642e-06 * meter / second}}, {'ibc0': {'y': 2.8530642e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00028593 * meter / second}}] {'ibc1': {'y': 0.00028593 * meter / second}}] \n", + "\n", + "Best trainer at step 31200:\n", + " train loss: 7.45e-04\n", + " test loss: 7.40e-04\n", + " test metric: []\n", + "\n", + "'train' took 4.693850 s\n", + "\n", + "Mean residual: 0.014 * (meter / second) / second\n", + "Adding new point: {'t': ArrayImpl([0.40964028], dtype=float32) * second, 'x': ArrayImpl([-0.00796556], dtype=float32) * meter} \n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.013628 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "32000 [0.00079346 * 10.0^0 * ((meter / second) / second) ** 2, [0.00050915 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.8530642e-06 * meter / second}}, {'ibc0': {'y': 2.8530642e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00028593 * meter / second}}] {'ibc1': {'y': 0.00028593 * meter / second}}] \n", + "33000 [0.00055445 * 10.0^0 * ((meter / second) / second) ** 2, [0.0004924 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.0238429e-06 * meter / second}}, {'ibc0': {'y': 2.0238429e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029025 * meter / second}}] {'ibc1': {'y': 0.00029025 * meter / second}}] \n", + "34000 [0.00052658 * 10.0^0 * ((meter / second) / second) ** 2, [0.00047557 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.0058028e-06 * meter / second}}, {'ibc0': {'y': 2.0058028e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029186 * meter / second}}] {'ibc1': {'y': 0.00029186 * meter / second}}] \n", + "35000 [0.00050164 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045865 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.9805689e-06 * meter / second}}, {'ibc0': {'y': 1.9805689e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0002901 * meter / second}}] {'ibc1': {'y': 0.0002901 * meter / second}}] \n", + "Epoch 35000: early stopping\n", + "\n", + "Best trainer at step 35000:\n", + " train loss: 7.94e-04\n", + " test loss: 7.51e-04\n", + " test metric: []\n", + "\n", + "'train' took 11.863162 s\n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.009882 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "35000 [0.00050164 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045865 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.9805689e-06 * meter / second}}, {'ibc0': {'y': 1.9805689e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0002901 * meter / second}}] {'ibc1': {'y': 0.0002901 * meter / second}}] \n", + "35100 [0.00050166 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045857 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.9694924e-06 * meter / second}}, {'ibc0': {'y': 1.9694924e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029009 * meter / second}}] {'ibc1': {'y': 0.00029009 * meter / second}}] \n", + "35200 [0.00050164 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045859 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.9775282e-06 * meter / second}}, {'ibc0': {'y': 1.9775282e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0002901 * meter / second}}] {'ibc1': {'y': 0.0002901 * meter / second}}] \n", + "35300 [0.00050156 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045861 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.0046225e-06 * meter / second}}, {'ibc0': {'y': 2.0046225e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029016 * meter / second}}] {'ibc1': {'y': 0.00029016 * meter / second}}] \n", + "35400 [0.00050155 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045858 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.0021143e-06 * meter / second}}, {'ibc0': {'y': 2.0021143e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029016 * meter / second}}] {'ibc1': {'y': 0.00029016 * meter / second}}] \n", + "35500 [0.00050156 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045858 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.0010755e-06 * meter / second}}, {'ibc0': {'y': 2.0010755e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029016 * meter / second}}] {'ibc1': {'y': 0.00029016 * meter / second}}] \n", + "35600 [0.00050155 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045855 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.9991612e-06 * meter / second}}, {'ibc0': {'y': 1.9991612e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029016 * meter / second}}] {'ibc1': {'y': 0.00029016 * meter / second}}] \n", + "35700 [0.00050155 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045855 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.9982401e-06 * meter / second}}, {'ibc0': {'y': 1.9982401e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029016 * meter / second}}] {'ibc1': {'y': 0.00029016 * meter / second}}] \n", + "35800 [0.00050156 * 10.0^0 * ((meter / second) / second) ** 2, [0.0004586 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.9993226e-06 * meter / second}}, {'ibc0': {'y': 1.9993226e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029015 * meter / second}}] {'ibc1': {'y': 0.00029015 * meter / second}}] \n", + "35900 [0.00050156 * 10.0^0 * ((meter / second) / second) ** 2, [0.0004586 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.9988458e-06 * meter / second}}, {'ibc0': {'y': 1.9988458e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029015 * meter / second}}] {'ibc1': {'y': 0.00029015 * meter / second}}] \n", + "36000 [0.00050155 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045858 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.9998658e-06 * meter / second}}, {'ibc0': {'y': 1.9998658e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029015 * meter / second}}] {'ibc1': {'y': 0.00029015 * meter / second}}] \n", + "\n", + "Best trainer at step 36000:\n", + " train loss: 7.94e-04\n", + " test loss: 7.51e-04\n", + " test metric: []\n", + "\n", + "'train' took 4.908738 s\n", + "\n", + "Mean residual: 0.013 * (meter / second) / second\n", + "Adding new point: {'t': ArrayImpl([0.2315986], dtype=float32) * second, 'x': ArrayImpl([-0.00680643], dtype=float32) * meter} \n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.015565 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "36000 [0.00074802 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045858 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.9998658e-06 * meter / second}}, {'ibc0': {'y': 1.9998658e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029015 * meter / second}}] {'ibc1': {'y': 0.00029015 * meter / second}}] \n", + "37000 [0.00059534 * 10.0^0 * ((meter / second) / second) ** 2, [0.00048061 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.9475647e-06 * meter / second}}, {'ibc0': {'y': 1.9475647e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00031009 * meter / second}}] {'ibc1': {'y': 0.00031009 * meter / second}}] \n", + "38000 [0.0005734 * 10.0^0 * ((meter / second) / second) ** 2, [0.00047273 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.9098984e-06 * meter / second}}, {'ibc0': {'y': 1.9098984e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00030421 * meter / second}}] {'ibc1': {'y': 0.00030421 * meter / second}}] \n", + "39000 [0.00054813 * 10.0^0 * ((meter / second) / second) ** 2, [0.00046036 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.8778497e-06 * meter / second}}, {'ibc0': {'y': 1.8778497e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029654 * meter / second}}] {'ibc1': {'y': 0.00029654 * meter / second}}] \n", + "Epoch 39000: early stopping\n", + "\n", + "Best trainer at step 39000:\n", + " train loss: 8.47e-04\n", + " test loss: 7.59e-04\n", + " test metric: []\n", + "\n", + "'train' took 12.797805 s\n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.010421 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "39000 [0.00054813 * 10.0^0 * ((meter / second) / second) ** 2, [0.00046036 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.8778497e-06 * meter / second}}, {'ibc0': {'y': 1.8778497e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029654 * meter / second}}] {'ibc1': {'y': 0.00029654 * meter / second}}] \n", + "39100 [0.00054806 * 10.0^0 * ((meter / second) / second) ** 2, [0.00046043 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.870236e-06 * meter / second}}, {'ibc0': {'y': 1.870236e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029661 * meter / second}}] {'ibc1': {'y': 0.00029661 * meter / second}}] \n", + "39200 [0.00054929 * 10.0^0 * ((meter / second) / second) ** 2, [0.0004634 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.0574782e-06 * meter / second}}, {'ibc0': {'y': 2.0574782e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029533 * meter / second}}] {'ibc1': {'y': 0.00029533 * meter / second}}] \n", + "39300 [0.00054904 * 10.0^0 * ((meter / second) / second) ** 2, [0.00046287 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.0242942e-06 * meter / second}}, {'ibc0': {'y': 2.0242942e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029551 * meter / second}}] {'ibc1': {'y': 0.00029551 * meter / second}}] \n", + "39400 [0.00054891 * 10.0^0 * ((meter / second) / second) ** 2, [0.00046254 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.004753e-06 * meter / second}}, {'ibc0': {'y': 2.004753e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029562 * meter / second}}] {'ibc1': {'y': 0.00029562 * meter / second}}] \n", + "39500 [0.00054882 * 10.0^0 * ((meter / second) / second) ** 2, [0.0004622 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.994075e-06 * meter / second}}, {'ibc0': {'y': 1.994075e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0002957 * meter / second}}] {'ibc1': {'y': 0.0002957 * meter / second}}] \n", + "39600 [0.0005721 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045579 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.6710437e-06 * meter / second}}, {'ibc0': {'y': 1.6710437e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00030883 * meter / second}}] {'ibc1': {'y': 0.00030883 * meter / second}}] \n", + "39700 [0.00056654 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045358 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.5904287e-06 * meter / second}}, {'ibc0': {'y': 1.5904287e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00030726 * meter / second}}] {'ibc1': {'y': 0.00030726 * meter / second}}] \n", + "39800 [0.00056229 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045216 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.5325267e-06 * meter / second}}, {'ibc0': {'y': 1.5325267e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00030581 * meter / second}}] {'ibc1': {'y': 0.00030581 * meter / second}}] \n", + "39900 [0.0005591 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045143 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.498971e-06 * meter / second}}, {'ibc0': {'y': 1.498971e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00030449 * meter / second}}] {'ibc1': {'y': 0.00030449 * meter / second}}] \n", + "40000 [0.00055651 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045115 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.4806845e-06 * meter / second}}, {'ibc0': {'y': 1.4806845e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00030329 * meter / second}}] {'ibc1': {'y': 0.00030329 * meter / second}}] \n", + "\n", + "Best trainer at step 39500:\n", + " train loss: 8.47e-04\n", + " test loss: 7.60e-04\n", + " test metric: []\n", + "\n", + "'train' took 4.848265 s\n", + "\n", + "Mean residual: 0.013 * (meter / second) / second\n", + "Adding new point: {'t': ArrayImpl([0.98284292], dtype=float32) * second, 'x': ArrayImpl([0.00254142], dtype=float32) * meter} \n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.014243 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "40000 [0.0006681 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045115 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.4806845e-06 * meter / second}}, {'ibc0': {'y': 1.4806845e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00030329 * meter / second}}] {'ibc1': {'y': 0.00030329 * meter / second}}] \n", + "41000 [0.00057995 * 10.0^0 * ((meter / second) / second) ** 2, [0.00048127 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.0367063e-06 * meter / second}}, {'ibc0': {'y': 2.0367063e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029667 * meter / second}}] {'ibc1': {'y': 0.00029667 * meter / second}}] \n", + "42000 [0.00055732 * 10.0^0 * ((meter / second) / second) ** 2, [0.000462 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.8838784e-06 * meter / second}}, {'ibc0': {'y': 1.8838784e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0002966 * meter / second}}] {'ibc1': {'y': 0.0002966 * meter / second}}] \n", + "43000 [0.0005333 * 10.0^0 * ((meter / second) / second) ** 2, [0.00044418 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.8350134e-06 * meter / second}}, {'ibc0': {'y': 1.8350134e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00029156 * meter / second}}] {'ibc1': {'y': 0.00029156 * meter / second}}] \n", + "44000 [0.00050091 * 10.0^0 * ((meter / second) / second) ** 2, [0.0004224 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.826639e-06 * meter / second}}, {'ibc0': {'y': 1.826639e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027955 * meter / second}}] {'ibc1': {'y': 0.00027955 * meter / second}}] \n", + "Epoch 44000: early stopping\n", + "\n", + "Best trainer at step 44000:\n", + " train loss: 7.82e-04\n", + " test loss: 7.04e-04\n", + " test metric: []\n", + "\n", + "'train' took 14.967950 s\n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.009629 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "44000 [0.00050091 * 10.0^0 * ((meter / second) / second) ** 2, [0.0004224 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.826639e-06 * meter / second}}, {'ibc0': {'y': 1.826639e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027955 * meter / second}}] {'ibc1': {'y': 0.00027955 * meter / second}}] \n", + "44100 [0.00050114 * 10.0^0 * ((meter / second) / second) ** 2, [0.00042319 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.8824794e-06 * meter / second}}, {'ibc0': {'y': 1.8824794e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027945 * meter / second}}] {'ibc1': {'y': 0.00027945 * meter / second}}] \n", + "44200 [0.00145139 * 10.0^0 * ((meter / second) / second) ** 2, [0.00122295 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 8.942031e-06 * meter / second}}, {'ibc0': {'y': 8.942031e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027929 * meter / second}}] {'ibc1': {'y': 0.00027929 * meter / second}}] \n", + "44300 [0.00127814 * 10.0^0 * ((meter / second) / second) ** 2, [0.00108249 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 7.864425e-06 * meter / second}}, {'ibc0': {'y': 7.864425e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027888 * meter / second}}] {'ibc1': {'y': 0.00027888 * meter / second}}] \n", + "44400 [0.00113658 * 10.0^0 * ((meter / second) / second) ** 2, [0.00096735 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 6.9546295e-06 * meter / second}}, {'ibc0': {'y': 6.9546295e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027857 * meter / second}}] {'ibc1': {'y': 0.00027857 * meter / second}}] \n", + "44500 [0.00102089 * 10.0^0 * ((meter / second) / second) ** 2, [0.00087287 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 6.1936867e-06 * meter / second}}, {'ibc0': {'y': 6.1936867e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027836 * meter / second}}] {'ibc1': {'y': 0.00027836 * meter / second}}] \n", + "44600 [0.00092632 * 10.0^0 * ((meter / second) / second) ** 2, [0.00079524 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 5.5573573e-06 * meter / second}}, {'ibc0': {'y': 5.5573573e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027821 * meter / second}}] {'ibc1': {'y': 0.00027821 * meter / second}}] \n", + "44700 [0.00084903 * 10.0^0 * ((meter / second) / second) ** 2, [0.00073138 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 5.0196286e-06 * meter / second}}, {'ibc0': {'y': 5.0196286e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027812 * meter / second}}] {'ibc1': {'y': 0.00027812 * meter / second}}] \n", + "44800 [0.0007858 * 10.0^0 * ((meter / second) / second) ** 2, [0.00067878 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.56894e-06 * meter / second}}, {'ibc0': {'y': 4.56894e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027808 * meter / second}}] {'ibc1': {'y': 0.00027808 * meter / second}}] \n", + "44900 [0.00073408 * 10.0^0 * ((meter / second) / second) ** 2, [0.00063543 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.191006e-06 * meter / second}}, {'ibc0': {'y': 4.191006e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027807 * meter / second}}] {'ibc1': {'y': 0.00027807 * meter / second}}] \n", + "45000 [0.00069176 * 10.0^0 * ((meter / second) / second) ** 2, [0.00059965 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 3.8737767e-06 * meter / second}}, {'ibc0': {'y': 3.8737767e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027808 * meter / second}}] {'ibc1': {'y': 0.00027808 * meter / second}}] \n", + "\n", + "Best trainer at step 44000:\n", + " train loss: 7.82e-04\n", + " test loss: 7.04e-04\n", + " test metric: []\n", + "\n", + "'train' took 4.975001 s\n", + "\n", + "Mean residual: 0.014 * (meter / second) / second\n", + "Adding new point: {'t': ArrayImpl([0.47824991], dtype=float32) * second, 'x': ArrayImpl([0.00034535], dtype=float32) * meter} \n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.013878 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "45000 [0.00086286 * 10.0^0 * ((meter / second) / second) ** 2, [0.00059965 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 3.8737767e-06 * meter / second}}, {'ibc0': {'y': 3.8737767e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027808 * meter / second}}] {'ibc1': {'y': 0.00027808 * meter / second}}] \n", + "46000 [0.00051184 * 10.0^0 * ((meter / second) / second) ** 2, [0.00043078 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.951535e-06 * meter / second}}, {'ibc0': {'y': 1.951535e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00028326 * meter / second}}] {'ibc1': {'y': 0.00028326 * meter / second}}] \n", + "47000 [0.00049468 * 10.0^0 * ((meter / second) / second) ** 2, [0.00041779 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.8175754e-06 * meter / second}}, {'ibc0': {'y': 1.8175754e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027674 * meter / second}}] {'ibc1': {'y': 0.00027674 * meter / second}}] \n", + "48000 [0.00047711 * 10.0^0 * ((meter / second) / second) ** 2, [0.00040669 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.8042014e-06 * meter / second}}, {'ibc0': {'y': 1.8042014e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00026785 * meter / second}}] {'ibc1': {'y': 0.00026785 * meter / second}}] \n", + "Epoch 48000: early stopping\n", + "\n", + "Best trainer at step 48000:\n", + " train loss: 7.47e-04\n", + " test loss: 6.76e-04\n", + " test metric: []\n", + "\n", + "'train' took 11.456536 s\n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.009981 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "48000 [0.00047711 * 10.0^0 * ((meter / second) / second) ** 2, [0.00040669 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.8042014e-06 * meter / second}}, {'ibc0': {'y': 1.8042014e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00026785 * meter / second}}] {'ibc1': {'y': 0.00026785 * meter / second}}] \n", + "48100 [0.00047705 * 10.0^0 * ((meter / second) / second) ** 2, [0.00040699 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.8382888e-06 * meter / second}}, {'ibc0': {'y': 1.8382888e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00026787 * meter / second}}] {'ibc1': {'y': 0.00026787 * meter / second}}] \n", + "48200 [0.00047711 * 10.0^0 * ((meter / second) / second) ** 2, [0.00040684 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.838244e-06 * meter / second}}, {'ibc0': {'y': 1.838244e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00026778 * meter / second}}] {'ibc1': {'y': 0.00026778 * meter / second}}] \n", + "48300 [0.00055811 * 10.0^0 * ((meter / second) / second) ** 2, [0.00051886 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.0354166e-06 * meter / second}}, {'ibc0': {'y': 2.0354166e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027301 * meter / second}}] {'ibc1': {'y': 0.00027301 * meter / second}}] \n", + "48400 [0.00054285 * 10.0^0 * ((meter / second) / second) ** 2, [0.00050191 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.7836052e-06 * meter / second}}, {'ibc0': {'y': 1.7836052e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027229 * meter / second}}] {'ibc1': {'y': 0.00027229 * meter / second}}] \n", + "48500 [0.00053009 * 10.0^0 * ((meter / second) / second) ** 2, [0.00048734 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.5927877e-06 * meter / second}}, {'ibc0': {'y': 1.5927877e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027169 * meter / second}}] {'ibc1': {'y': 0.00027169 * meter / second}}] \n", + "48600 [0.00051951 * 10.0^0 * ((meter / second) / second) ** 2, [0.0004748 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.4500241e-06 * meter / second}}, {'ibc0': {'y': 1.4500241e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027117 * meter / second}}] {'ibc1': {'y': 0.00027117 * meter / second}}] \n", + "48700 [0.00051096 * 10.0^0 * ((meter / second) / second) ** 2, [0.00046426 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.344583e-06 * meter / second}}, {'ibc0': {'y': 1.344583e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027073 * meter / second}}] {'ibc1': {'y': 0.00027073 * meter / second}}] \n", + "48800 [0.0005042 * 10.0^0 * ((meter / second) / second) ** 2, [0.00045563 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.2793502e-06 * meter / second}}, {'ibc0': {'y': 1.2793502e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027043 * meter / second}}] {'ibc1': {'y': 0.00027043 * meter / second}}] \n", + "48900 [0.00049869 * 10.0^0 * ((meter / second) / second) ** 2, [0.00044829 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.239052e-06 * meter / second}}, {'ibc0': {'y': 1.239052e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027017 * meter / second}}] {'ibc1': {'y': 0.00027017 * meter / second}}] \n", + "49000 [0.00049421 * 10.0^0 * ((meter / second) / second) ** 2, [0.00044207 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.218723e-06 * meter / second}}, {'ibc0': {'y': 1.218723e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00026993 * meter / second}}] {'ibc1': {'y': 0.00026993 * meter / second}}] \n", + "\n", + "Best trainer at step 48200:\n", + " train loss: 7.47e-04\n", + " test loss: 6.76e-04\n", + " test metric: []\n", + "\n", + "'train' took 4.382472 s\n", + "\n", + "Mean residual: 0.013 * (meter / second) / second\n", + "Adding new point: {'t': ArrayImpl([0.32790023], dtype=float32) * second, 'x': ArrayImpl([-0.00789118], dtype=float32) * meter} \n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.013897 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "49000 [0.00057817 * 10.0^0 * ((meter / second) / second) ** 2, [0.00044207 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.218723e-06 * meter / second}}, {'ibc0': {'y': 1.218723e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00026993 * meter / second}}] {'ibc1': {'y': 0.00026993 * meter / second}}] \n", + "50000 [0.00050032 * 10.0^0 * ((meter / second) / second) ** 2, [0.00041502 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.859967e-06 * meter / second}}, {'ibc0': {'y': 1.859967e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00028114 * meter / second}}] {'ibc1': {'y': 0.00028114 * meter / second}}] \n", + "51000 [0.00047413 * 10.0^0 * ((meter / second) / second) ** 2, [0.0004074 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.8621943e-06 * meter / second}}, {'ibc0': {'y': 1.8621943e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00027061 * meter / second}}] {'ibc1': {'y': 0.00027061 * meter / second}}] \n", + "52000 [0.00043118 * 10.0^0 * ((meter / second) / second) ** 2, [0.00039883 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.9477718e-06 * meter / second}}, {'ibc0': {'y': 1.9477718e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00025804 * meter / second}}] {'ibc1': {'y': 0.00025804 * meter / second}}] \n", + "53000 [0.00039573 * 10.0^0 * ((meter / second) / second) ** 2, [0.00037706 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.8887133e-06 * meter / second}}, {'ibc0': {'y': 1.8887133e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00023655 * meter / second}}] {'ibc1': {'y': 0.00023655 * meter / second}}] \n", + "54000 [0.00036355 * 10.0^0 * ((meter / second) / second) ** 2, [0.00035133 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.6823096e-06 * meter / second}}, {'ibc0': {'y': 1.6823096e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00021243 * meter / second}}] {'ibc1': {'y': 0.00021243 * meter / second}}] \n", + "55000 [0.00035543 * 10.0^0 * ((meter / second) / second) ** 2, [0.0003454 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.3884645e-06 * meter / second}}, {'ibc0': {'y': 1.3884645e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00019187 * meter / second}}] {'ibc1': {'y': 0.00019187 * meter / second}}] \n", + "Epoch 55000: early stopping\n", + "\n", + "Best trainer at step 55000:\n", + " train loss: 5.49e-04\n", + " test loss: 5.39e-04\n", + " test metric: []\n", + "\n", + "'train' took 28.337766 s\n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.010395 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "55000 [0.00035543 * 10.0^0 * ((meter / second) / second) ** 2, [0.0003454 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.3884645e-06 * meter / second}}, {'ibc0': {'y': 1.3884645e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00019187 * meter / second}}] {'ibc1': {'y': 0.00019187 * meter / second}}] \n", + "55100 [0.00038491 * 10.0^0 * ((meter / second) / second) ** 2, [0.00036448 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.1007363e-06 * meter / second}}, {'ibc0': {'y': 2.1007363e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00019324 * meter / second}}] {'ibc1': {'y': 0.00019324 * meter / second}}] \n", + "55200 [0.00037617 * 10.0^0 * ((meter / second) / second) ** 2, [0.00035767 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.0267723e-06 * meter / second}}, {'ibc0': {'y': 2.0267723e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00019314 * meter / second}}] {'ibc1': {'y': 0.00019314 * meter / second}}] \n", + "55300 [0.00036902 * 10.0^0 * ((meter / second) / second) ** 2, [0.00035212 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.9594597e-06 * meter / second}}, {'ibc0': {'y': 1.9594597e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00019307 * meter / second}}] {'ibc1': {'y': 0.00019307 * meter / second}}] \n", + "55400 [0.00036314 * 10.0^0 * ((meter / second) / second) ** 2, [0.00034759 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.9019135e-06 * meter / second}}, {'ibc0': {'y': 1.9019135e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00019301 * meter / second}}] {'ibc1': {'y': 0.00019301 * meter / second}}] \n", + "55500 [0.00035832 * 10.0^0 * ((meter / second) / second) ** 2, [0.00034388 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.8527855e-06 * meter / second}}, {'ibc0': {'y': 1.8527855e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00019295 * meter / second}}] {'ibc1': {'y': 0.00019295 * meter / second}}] \n", + "55600 [0.00035437 * 10.0^0 * ((meter / second) / second) ** 2, [0.00034088 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.8089495e-06 * meter / second}}, {'ibc0': {'y': 1.8089495e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00019291 * meter / second}}] {'ibc1': {'y': 0.00019291 * meter / second}}] \n", + "55700 [0.00035103 * 10.0^0 * ((meter / second) / second) ** 2, [0.00033836 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.7687397e-06 * meter / second}}, {'ibc0': {'y': 1.7687397e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00019289 * meter / second}}] {'ibc1': {'y': 0.00019289 * meter / second}}] \n", + "55800 [0.00034844 * 10.0^0 * ((meter / second) / second) ** 2, [0.00033642 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.7341235e-06 * meter / second}}, {'ibc0': {'y': 1.7341235e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00019286 * meter / second}}] {'ibc1': {'y': 0.00019286 * meter / second}}] \n", + "55900 [0.00034628 * 10.0^0 * ((meter / second) / second) ** 2, [0.00033482 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.7029475e-06 * meter / second}}, {'ibc0': {'y': 1.7029475e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00019285 * meter / second}}] {'ibc1': {'y': 0.00019285 * meter / second}}] \n", + "56000 [0.00034438 * 10.0^0 * ((meter / second) / second) ** 2, [0.00033343 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.6735721e-06 * meter / second}}, {'ibc0': {'y': 1.6735721e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00019284 * meter / second}}] {'ibc1': {'y': 0.00019284 * meter / second}}] \n", + "\n", + "Best trainer at step 56000:\n", + " train loss: 5.39e-04\n", + " test loss: 5.28e-04\n", + " test metric: []\n", + "\n", + "'train' took 5.173902 s\n", + "\n", + "Mean residual: 0.012 * (meter / second) / second\n", + "Adding new point: {'t': ArrayImpl([0.5695765], dtype=float32) * second, 'x': ArrayImpl([-0.00540644], dtype=float32) * meter} \n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.015050 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "56000 [0.00045088 * 10.0^0 * ((meter / second) / second) ** 2, [0.00033343 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.6735721e-06 * meter / second}}, {'ibc0': {'y': 1.6735721e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00019284 * meter / second}}] {'ibc1': {'y': 0.00019284 * meter / second}}] \n", + "57000 [0.0003596 * 10.0^0 * ((meter / second) / second) ** 2, [0.00033415 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.4792597e-06 * meter / second}}, {'ibc0': {'y': 1.4792597e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00019963 * meter / second}}] {'ibc1': {'y': 0.00019963 * meter / second}}] \n", + "58000 [0.00034447 * 10.0^0 * ((meter / second) / second) ** 2, [0.0003254 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.3338099e-06 * meter / second}}, {'ibc0': {'y': 1.3338099e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0001965 * meter / second}}] {'ibc1': {'y': 0.0001965 * meter / second}}] \n", + "59000 [0.00033271 * 10.0^0 * ((meter / second) / second) ** 2, [0.00031697 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.3009029e-06 * meter / second}}, {'ibc0': {'y': 1.3009029e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00019046 * meter / second}}] {'ibc1': {'y': 0.00019046 * meter / second}}] \n", + "60000 [0.00031924 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030644 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.2355371e-06 * meter / second}}, {'ibc0': {'y': 1.2355371e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00018091 * meter / second}}] {'ibc1': {'y': 0.00018091 * meter / second}}] \n", + "Epoch 60000: early stopping\n", + "\n", + "Best trainer at step 60000:\n", + " train loss: 5.01e-04\n", + " test loss: 4.89e-04\n", + " test metric: []\n", + "\n", + "'train' took 16.605614 s\n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.009775 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "60000 [0.00031924 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030644 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.2355371e-06 * meter / second}}, {'ibc0': {'y': 1.2355371e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00018091 * meter / second}}] {'ibc1': {'y': 0.00018091 * meter / second}}] \n", + "60100 [0.00031926 * 10.0^0 * ((meter / second) / second) ** 2, [0.0003067 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.2158225e-06 * meter / second}}, {'ibc0': {'y': 1.2158225e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00018093 * meter / second}}] {'ibc1': {'y': 0.00018093 * meter / second}}] \n", + "60200 [0.0003193 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030668 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.2317463e-06 * meter / second}}, {'ibc0': {'y': 1.2317463e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00018085 * meter / second}}] {'ibc1': {'y': 0.00018085 * meter / second}}] \n", + "60300 [0.00032016 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030574 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 8.9220623e-07 * meter / second}}, {'ibc0': {'y': 8.9220623e-07 * meter / second}}, \n", + " {'ibc1': {'y': 0.0001815 * meter / second}}] {'ibc1': {'y': 0.0001815 * meter / second}}] \n", + "60400 [0.00031992 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030578 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 9.2139237e-07 * meter / second}}, {'ibc0': {'y': 9.2139237e-07 * meter / second}}, \n", + " {'ibc1': {'y': 0.00018143 * meter / second}}] {'ibc1': {'y': 0.00018143 * meter / second}}] \n", + "60500 [0.00031974 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030583 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 9.5220133e-07 * meter / second}}, {'ibc0': {'y': 9.5220133e-07 * meter / second}}, \n", + " {'ibc1': {'y': 0.00018136 * meter / second}}] {'ibc1': {'y': 0.00018136 * meter / second}}] \n", + "60600 [0.00031961 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030594 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 9.865097e-07 * meter / second}}, {'ibc0': {'y': 9.865097e-07 * meter / second}}, \n", + " {'ibc1': {'y': 0.00018126 * meter / second}}] {'ibc1': {'y': 0.00018126 * meter / second}}] \n", + "60700 [0.00031952 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030598 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.0199747e-06 * meter / second}}, {'ibc0': {'y': 1.0199747e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00018119 * meter / second}}] {'ibc1': {'y': 0.00018119 * meter / second}}] \n", + "60800 [0.00031941 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030598 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.0453716e-06 * meter / second}}, {'ibc0': {'y': 1.0453716e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00018118 * meter / second}}] {'ibc1': {'y': 0.00018118 * meter / second}}] \n", + "60900 [0.00031924 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030594 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.0795525e-06 * meter / second}}, {'ibc0': {'y': 1.0795525e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0001812 * meter / second}}] {'ibc1': {'y': 0.0001812 * meter / second}}] \n", + "61000 [0.00040084 * 10.0^0 * ((meter / second) / second) ** 2, [0.00037745 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.2552299e-05 * meter / second}}, {'ibc0': {'y': 1.2552299e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017717 * meter / second}}] {'ibc1': {'y': 0.00017717 * meter / second}}] \n", + "\n", + "Best trainer at step 60200:\n", + " train loss: 5.01e-04\n", + " test loss: 4.89e-04\n", + " test metric: []\n", + "\n", + "'train' took 4.717136 s\n", + "\n", + "Mean residual: 0.012 * (meter / second) / second\n", + "Adding new point: {'t': ArrayImpl([0.38778442], dtype=float32) * second, 'x': ArrayImpl([-0.0043211], dtype=float32) * meter} \n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.015250 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "61000 [0.00046435 * 10.0^0 * ((meter / second) / second) ** 2, [0.00037745 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.2552299e-05 * meter / second}}, {'ibc0': {'y': 1.2552299e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017717 * meter / second}}] {'ibc1': {'y': 0.00017717 * meter / second}}] \n", + "62000 [0.00034305 * 10.0^0 * ((meter / second) / second) ** 2, [0.00031215 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.2617899e-06 * meter / second}}, {'ibc0': {'y': 1.2617899e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00018198 * meter / second}}] {'ibc1': {'y': 0.00018198 * meter / second}}] \n", + "63000 [0.0003293 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030744 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1898037e-06 * meter / second}}, {'ibc0': {'y': 1.1898037e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017979 * meter / second}}] {'ibc1': {'y': 0.00017979 * meter / second}}] \n", + "64000 [0.00032155 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030236 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1578732e-06 * meter / second}}, {'ibc0': {'y': 1.1578732e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017604 * meter / second}}] {'ibc1': {'y': 0.00017604 * meter / second}}] \n", + "Epoch 64000: early stopping\n", + "\n", + "Best trainer at step 64000:\n", + " train loss: 4.99e-04\n", + " test loss: 4.80e-04\n", + " test metric: []\n", + "\n", + "'train' took 11.294281 s\n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.010299 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "64000 [0.00032155 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030236 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1578732e-06 * meter / second}}, {'ibc0': {'y': 1.1578732e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017604 * meter / second}}] {'ibc1': {'y': 0.00017604 * meter / second}}] \n", + "64100 [0.00032129 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030189 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.2672714e-06 * meter / second}}, {'ibc0': {'y': 1.2672714e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017607 * meter / second}}] {'ibc1': {'y': 0.00017607 * meter / second}}] \n", + "64200 [0.00032125 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030183 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.230208e-06 * meter / second}}, {'ibc0': {'y': 1.230208e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017615 * meter / second}}] {'ibc1': {'y': 0.00017615 * meter / second}}] \n", + "64300 [0.00032105 * 10.0^0 * ((meter / second) / second) ** 2, [0.0003016 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1040507e-06 * meter / second}}, {'ibc0': {'y': 1.1040507e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0001765 * meter / second}}] {'ibc1': {'y': 0.0001765 * meter / second}}] \n", + "64400 [0.00032116 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030174 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1353521e-06 * meter / second}}, {'ibc0': {'y': 1.1353521e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017633 * meter / second}}] {'ibc1': {'y': 0.00017633 * meter / second}}] \n", + "64500 [0.00032118 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030177 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1384761e-06 * meter / second}}, {'ibc0': {'y': 1.1384761e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0001763 * meter / second}}] {'ibc1': {'y': 0.0001763 * meter / second}}] \n", + "64600 [0.00032113 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030171 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1360961e-06 * meter / second}}, {'ibc0': {'y': 1.1360961e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017638 * meter / second}}] {'ibc1': {'y': 0.00017638 * meter / second}}] \n", + "64700 [0.00032106 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030168 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1283665e-06 * meter / second}}, {'ibc0': {'y': 1.1283665e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017646 * meter / second}}] {'ibc1': {'y': 0.00017646 * meter / second}}] \n", + "64800 [0.00032214 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030261 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1278934e-06 * meter / second}}, {'ibc0': {'y': 1.1278934e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017566 * meter / second}}] {'ibc1': {'y': 0.00017566 * meter / second}}] \n", + "64900 [0.00032201 * 10.0^0 * ((meter / second) / second) ** 2, [0.0003025 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1321267e-06 * meter / second}}, {'ibc0': {'y': 1.1321267e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0001757 * meter / second}}] {'ibc1': {'y': 0.0001757 * meter / second}}] \n", + "65000 [0.00032184 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030237 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1423148e-06 * meter / second}}, {'ibc0': {'y': 1.1423148e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017577 * meter / second}}] {'ibc1': {'y': 0.00017577 * meter / second}}] \n", + "\n", + "Best trainer at step 64500:\n", + " train loss: 4.99e-04\n", + " test loss: 4.79e-04\n", + " test metric: []\n", + "\n", + "'train' took 4.623570 s\n", + "\n", + "Mean residual: 0.012 * (meter / second) / second\n", + "Adding new point: {'t': ArrayImpl([0.40250915], dtype=float32) * second, 'x': ArrayImpl([-0.010427], dtype=float32) * meter} \n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.014968 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "65000 [0.00039208 * 10.0^0 * ((meter / second) / second) ** 2, [0.00030237 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1423148e-06 * meter / second}}, {'ibc0': {'y': 1.1423148e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017577 * meter / second}}] {'ibc1': {'y': 0.00017577 * meter / second}}] \n", + "66000 [0.00035875 * 10.0^0 * ((meter / second) / second) ** 2, [0.00032071 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.144454e-06 * meter / second}}, {'ibc0': {'y': 1.144454e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00018135 * meter / second}}] {'ibc1': {'y': 0.00018135 * meter / second}}] \n", + "67000 [0.00034588 * 10.0^0 * ((meter / second) / second) ** 2, [0.00031595 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.0716824e-06 * meter / second}}, {'ibc0': {'y': 1.0716824e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017891 * meter / second}}] {'ibc1': {'y': 0.00017891 * meter / second}}] \n", + "Epoch 67001: early stopping\n", + "\n", + "Best trainer at step 67000:\n", + " train loss: 5.26e-04\n", + " test loss: 4.96e-04\n", + " test metric: []\n", + "\n", + "'train' took 7.938136 s\n", + "\n", + "Compiling trainer...\n", + "'compile' took 0.014745 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "67001 [0.00034587 * 10.0^0 * ((meter / second) / second) ** 2, [0.00031594 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.0716063e-06 * meter / second}}, {'ibc0': {'y': 1.0716063e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017891 * meter / second}}] {'ibc1': {'y': 0.00017891 * meter / second}}] \n", + "67100 [0.00034577 * 10.0^0 * ((meter / second) / second) ** 2, [0.00031621 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.0872557e-06 * meter / second}}, {'ibc0': {'y': 1.0872557e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.000179 * meter / second}}] {'ibc1': {'y': 0.000179 * meter / second}}] \n", + "67200 [0.00034568 * 10.0^0 * ((meter / second) / second) ** 2, [0.000316 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.0810584e-06 * meter / second}}, {'ibc0': {'y': 1.0810584e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017908 * meter / second}}] {'ibc1': {'y': 0.00017908 * meter / second}}] \n", + "67300 [0.00034568 * 10.0^0 * ((meter / second) / second) ** 2, [0.00031598 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.0880661e-06 * meter / second}}, {'ibc0': {'y': 1.0880661e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017907 * meter / second}}] {'ibc1': {'y': 0.00017907 * meter / second}}] \n", + "67400 [0.00034624 * 10.0^0 * ((meter / second) / second) ** 2, [0.00031566 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1337318e-06 * meter / second}}, {'ibc0': {'y': 1.1337318e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017865 * meter / second}}] {'ibc1': {'y': 0.00017865 * meter / second}}] \n", + "67500 [0.00034618 * 10.0^0 * ((meter / second) / second) ** 2, [0.00031566 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1352137e-06 * meter / second}}, {'ibc0': {'y': 1.1352137e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017867 * meter / second}}] {'ibc1': {'y': 0.00017867 * meter / second}}] \n", + "67600 [0.00034612 * 10.0^0 * ((meter / second) / second) ** 2, [0.00031567 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1311693e-06 * meter / second}}, {'ibc0': {'y': 1.1311693e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.0001787 * meter / second}}] {'ibc1': {'y': 0.0001787 * meter / second}}] \n", + "67700 [0.00034608 * 10.0^0 * ((meter / second) / second) ** 2, [0.00031568 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1283073e-06 * meter / second}}, {'ibc0': {'y': 1.1283073e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017872 * meter / second}}] {'ibc1': {'y': 0.00017872 * meter / second}}] \n", + "67800 [0.00034614 * 10.0^0 * ((meter / second) / second) ** 2, [0.00031567 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1323336e-06 * meter / second}}, {'ibc0': {'y': 1.1323336e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017869 * meter / second}}] {'ibc1': {'y': 0.00017869 * meter / second}}] \n", + "67900 [0.00034607 * 10.0^0 * ((meter / second) / second) ** 2, [0.00031569 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1263944e-06 * meter / second}}, {'ibc0': {'y': 1.1263944e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017873 * meter / second}}] {'ibc1': {'y': 0.00017873 * meter / second}}] \n", + "68000 [0.00034603 * 10.0^0 * ((meter / second) / second) ** 2, [0.0003157 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1240935e-06 * meter / second}}, {'ibc0': {'y': 1.1240935e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017874 * meter / second}}] {'ibc1': {'y': 0.00017874 * meter / second}}] \n", + "68001 [0.00034604 * 10.0^0 * ((meter / second) / second) ** 2, [0.0003157 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.1240547e-06 * meter / second}}, {'ibc0': {'y': 1.1240547e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00017874 * meter / second}}] {'ibc1': {'y': 0.00017874 * meter / second}}] \n", + "\n", + "Best trainer at step 67300:\n", + " train loss: 5.26e-04\n", + " test loss: 4.96e-04\n", + " test metric: []\n", + "\n", + "'train' took 4.620428 s\n", + "\n" + ] + } + ], + "source": [ + "while u.get_magnitude(err) > 0.012:\n", + " f = trainer.predict(X, operator=pde)\n", + " err_eq = u.math.absolute(f)\n", + " err = u.math.mean(err_eq)\n", + " print(f\"Mean residual: {err:.3f}\")\n", + "\n", + " x_id = u.math.argmax(err_eq)\n", + " new_xs = jax.tree.map(lambda x: x[[x_id]], X)\n", + " print(\"Adding new point:\", new_xs, \"\\n\")\n", + " problem.add_anchors(new_xs)\n", + " early_stopping = deepxde.callbacks.EarlyStopping(min_delta=1e-4, patience=2000)\n", + " trainer.compile(bst.optim.Adam(1e-3)).train(iterations=10000,\n", + " disregard_previous_best=True,\n", + " callbacks=[early_stopping])\n", + " trainer.compile(bst.optim.LBFGS(1e-3)).train(1000, display_every=100)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's visualize and save the data." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving loss history to /Users/sichaohe/Documents/GitHub/pinnx/docs/examples-pinn-forward/loss.dat ...\n", + "Saving checkpoint into /Users/sichaohe/Documents/GitHub/pinnx/docs/examples-pinn-forward/loss.dat\n", + "Saving training data to /Users/sichaohe/Documents/GitHub/pinnx/docs/examples-pinn-forward/train.dat ...\n", + "Saving checkpoint into /Users/sichaohe/Documents/GitHub/pinnx/docs/examples-pinn-forward/train.dat\n", + "Saving test data to /Users/sichaohe/Documents/GitHub/pinnx/docs/examples-pinn-forward/test.dat ...\n", + "Saving checkpoint into /Users/sichaohe/Documents/GitHub/pinnx/docs/examples-pinn-forward/test.dat\n" + ] + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "trainer.saveplot(issave=True, isplot=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also test the model with the data:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [], + "source": [ + "def gen_testdata():\n", + " data = np.load(\"../dataset/Burgers.npz\")\n", + " t, x, exact = data[\"t\"], data[\"x\"], data[\"usol\"].T\n", + " xx, tt = np.meshgrid(x, t)\n", + " X = {'x': np.ravel(xx) * u.meter, 't': np.ravel(tt) * u.second}\n", + " y = exact.flatten()[:, None]\n", + " return X, y * uy" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean residual: 0.01163746 * (meter / second) / second\n", + "L2 relative error: 225.97165\n" + ] + } + ], + "source": [ + "X, y_true = gen_testdata()\n", + "y_pred = trainer.predict(X)\n", + "f = pde(X, y_pred)\n", + "print(\"Mean residual:\", u.math.mean(u.math.absolute(f)))\n", + "print(\"L2 relative error:\", deepxde.metrics.l2_relative_error(y_true, y_pred['y']))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "pinnx", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.11" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/docs/experimental_docs/unit-examples-forward/Burgers_RAR.py b/docs/experimental_docs/unit-examples-forward/Burgers_RAR.py new file mode 100644 index 000000000..5bab95d61 --- /dev/null +++ b/docs/experimental_docs/unit-examples-forward/Burgers_RAR.py @@ -0,0 +1,81 @@ +import brainstate as bst +import brainunit as u +import jax.tree +import numpy as np + +import deepxde.experimental as deepxde + +geom = deepxde.geometry.Interval(-1, 1) +timedomain = deepxde.geometry.TimeDomain(0, 0.99) +geomtime = deepxde.geometry.GeometryXTime(geom, timedomain) +geomtime = geomtime.to_dict_point(x=u.meter, t=u.second) + +net = deepxde.nn.Model( + deepxde.nn.DictToArray(x=u.meter, t=u.second), + deepxde.nn.FNN([2] + [20] * 3 + [1], "tanh", bst.init.KaimingUniform()), + deepxde.nn.ArrayToDict(y=u.meter / u.second), +) +v = 0.01 / u.math.pi * u.meter ** 2 / u.second + + +def pde(x, y): + jacobian = net.jacobian(x) + hessian = net.hessian(x, xi='x', xj='x') + + dy_x = jacobian['y']['x'] + dy_t = jacobian['y']['t'] + dy_xx = hessian['y']['x']['x'] + return dy_t + y['y'] * dy_x - v * dy_xx + + +bc = deepxde.icbc.DirichletBC(lambda x: {'y': 0 * u.meter / u.second}) +ic = deepxde.icbc.IC(lambda x: {'y': -u.math.sin(u.math.pi * x['x'] / u.meter) * u.meter / u.second}) + +problem = deepxde.problem.TimePDE( + geomtime, + pde, + [bc, ic], + net, + num_domain=2500, + num_boundary=100, + num_initial=160 +) + +trainer = deepxde.Trainer(problem) + +trainer.compile(bst.optim.Adam(1e-3)).train(iterations=10000) +trainer.compile(bst.optim.LBFGS(1e-3)).train(1000) + +X = geomtime.random_points(100000) +err = 1 +while u.get_magnitude(err) > 0.012: + f = trainer.predict(X, operator=pde) + err_eq = u.math.absolute(f) + err = u.math.mean(err_eq) + print(f"Mean residual: {err:.3f}") + + x_id = u.math.argmax(err_eq) + new_xs = jax.tree.map(lambda x: x[[x_id]], X) + print("Adding new point:", new_xs, "\n") + problem.add_anchors(new_xs) + early_stopping = deepxde.callbacks.EarlyStopping(min_delta=1e-4, patience=2000) + trainer.compile(bst.optim.Adam(1e-3)).train(iterations=10000, + disregard_previous_best=True, + callbacks=[early_stopping]) + trainer.compile(bst.optim.LBFGS(1e-3)).train(1000, display_every=100) + +trainer.saveplot(issave=True, isplot=True) + + +def gen_testdata(): + data = np.load("../dataset/Burgers.npz") + t, x, exact = data["t"], data["x"], data["usol"].T + xx, tt = np.meshgrid(x, t) + X = {'x': np.ravel(xx) * u.meter, 't': np.ravel(tt) * u.second} + y = {'y': exact.flatten() * u.meter / u.second} + return X, y + + +X, y_true = gen_testdata() +y_pred = trainer.predict(X) +print("L2 relative error:", deepxde.metrics.l2_relative_error(y_true, y_pred)) diff --git a/docs/experimental_docs/unit-examples-forward/Euler_beam.ipynb b/docs/experimental_docs/unit-examples-forward/Euler_beam.ipynb new file mode 100644 index 000000000..1dd7a143e --- /dev/null +++ b/docs/experimental_docs/unit-examples-forward/Euler_beam.ipynb @@ -0,0 +1,469 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Euler-Bernoulli Beam Equation\n", + "\n", + "## Problem setup\n", + "\n", + "We will solve a Euler beam problem:\n", + "\n", + "$$\n", + "EI\\frac{d^{4}u}{dx^{4}}=p, \\qquad x \\in [0, 1],\n", + "$$\n", + "\n", + "with two boundary conditions on the right boundary,\n", + "\n", + "$$\n", + "u''(1)=0, u'''(1)=0\n", + "$$\n", + "\n", + "and one Dirichlet boundary condition on the left boundary,\n", + "\n", + "$$\n", + "u(0)=0\n", + "$$\n", + "\n", + "along with one Neumann boundary condition on the left boundary,\n", + "\n", + "$$\n", + "u'(0)=0\n", + "$$\n", + "\n", + "The exact solution is $u(x) = -\\frac{1}{24}x^4+\\frac{1}{6}x^3-\\frac{1}{4}x^2.$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Dimensional Analysis\n", + "\n", + "### **Boundary Conditions:**\n", + "1. **Right Boundary (at $ x = 1 $):**\n", + "\n", + " $$\n", + " u''(1) = 0, \\quad u'''(1) = 0\n", + " $$\n", + "\n", + "2. **Left Boundary (at $ x = 0 $):**\n", + "\n", + " $$\n", + " u(0) = 0, \\quad u'(0) = 0\n", + " $$\n", + "\n", + "### **Assigning Physical Units:**\n", + "\n", + "Let's identify and assign physical units to each variable and parameter in the equation.\n", + "\n", + "| **Variable/Parameter** | **Symbol** | **Physical Quantity** | **Unit (SI)** | **Dimension** |\n", + "|------------------------|------------|-----------------------------------|---------------------|--------------------------|\n", + "| **Displacement** | $ u $ | Beam deflection | meters (m) | Length $[L]$ |\n", + "| **Position** | $ x $ | Spatial coordinate along the beam | meters (m) | Length $[L]$ |\n", + "| **Young's Modulus** | $ E $ | Material property (stiffness) | pascals (Pa) | Pressure $[M][L]^{-1}[T]^{-2}$ |\n", + "| **Second Moment of Area** | $ I $ | Geometric property of the beam | meters$^4$ (m$^4$) | Length $^4$ $[L]^4$ |\n", + "| **Flexural Rigidity** | $ EI $ | Product of $ E $ and $ I $ | newton-meter squared (N·m$^2$) | $[EI] = [E][I] = [M][L]^3[T]^{-2}$ |\n", + "| **Load per Unit Length** | $ p $ | Distributed load on the beam | newtons per meter (N/m) | Force per Length $[M][L][T]^{-2}[L]^{-1} = [M][T]^{-2}$ |\n", + "\n", + "### **Dimensional Consistency Check:**\n", + "\n", + "To ensure the equation is dimensionally consistent, both sides must have the same dimensions.\n", + "\n", + "1. **Left Side ($ EI \\frac{d^4 u}{dx^4} $):**\n", + " - $ EI $ has units of N·m$^2$ and dimensions $[M][L]^3[T]^{-2}$.\n", + " - $ \\frac{d^4 u}{dx^4} $ involves four derivatives with respect to $ x $, each introducing a factor of $[L]^{-1}$.\n", + " - Thus, $ \\frac{d^4 u}{dx^4} $ has dimensions $[L]^{-4} \\times [L] = [L]^{-3}$.\n", + " - Multiplying by $ EI $: $[M][L]^3[T]^{-2} \\times [L]^{-3} = [M][T]^{-2}$.\n", + "\n", + "2. **Right Side ($ p $):**\n", + " - $ p $ has units of N/m and dimensions $[M][T]^{-2}$.\n", + "\n", + "Both sides have the same dimensions $[M][T]^{-2}$, confirming dimensional consistency.\n", + "\n", + "### **Summary of Physical Units:**\n", + "\n", + "- **$ u $** (Displacement): meters (m)\n", + "- **$ x $** (Position): meters (m)\n", + "- **$ E $** (Young's Modulus): pascals (Pa) = N/m$^2$\n", + "- **$ I $** (Second Moment of Area): meters$^4$ (m$^4$)\n", + "- **$ EI $** (Flexural Rigidity): newton-meter squared (N·m$^2$)\n", + "- **$ p $** (Load per Unit Length): newtons per meter (N/m)\n", + "\n", + "### **Boundary Conditions Units:**\n", + "\n", + "1. **$ u''(1) = 0 $:**\n", + " - $ u'' $ involves two derivatives: $[L] \\times [L]^{-2} = [L]^{-1}$\n", + " - Units: 1/m\n", + "\n", + "2. **$ u'''(1) = 0 $:**\n", + " - $ u''' $ involves three derivatives: $[L] \\times [L]^{-3} = [L]^{-2}$\n", + " - Units: 1/m$^2$\n", + "\n", + "3. **$ u(0) = 0 $:**\n", + " - Units: meters (m)\n", + "\n", + "4. **$ u'(0) = 0 $:**\n", + " - $ u' $ involves one derivative: $[L] \\times [L]^{-1} = \\text{dimensionless}$ (often interpreted as radians in small-angle approximations)\n", + "\n", + "### **Conclusion:**\n", + "\n", + "All variables and parameters in the Euler-Bernoulli Beam Equation have been assigned consistent physical units, ensuring dimensional integrity of the equation and its boundary conditions.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code Implementation\n", + "\n", + "First, we import the necessary libraries and define the physical units for the problem." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T14:02:06.289401Z", + "start_time": "2024-12-17T14:02:02.480109Z" + } + }, + "outputs": [], + "source": [ + "import brainstate as bst\n", + "import brainunit as u\n", + "\n", + "import deepxde.experimental as deepxde" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the physical units for the problem." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T14:02:06.300312Z", + "start_time": "2024-12-17T14:02:06.295891Z" + } + }, + "outputs": [], + "source": [ + "unit_of_u = u.meter\n", + "unit_of_x = u.meter\n", + "unit_of_E = u.pascal\n", + "unit_of_I = u.meter ** 4\n", + "unit_of_p = u.kilogram / u.second ** 2\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the parameters for the problem." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T14:02:06.403154Z", + "start_time": "2024-12-17T14:02:06.386503Z" + } + }, + "outputs": [], + "source": [ + "E = 1 * unit_of_E\n", + "I = 1 * unit_of_I\n", + "p = -1. * unit_of_p\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the PDE for the Euler beam problem." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T14:02:06.423666Z", + "start_time": "2024-12-17T14:02:06.419808Z" + } + }, + "outputs": [], + "source": [ + "def pde(x, y):\n", + " dy_xxxx = net.gradient(x, order=4)['y']['x']['x']['x']['x']\n", + " return E * I * dy_xxxx - p" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the geometric domain for the problem." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T14:02:06.431507Z", + "start_time": "2024-12-17T14:02:06.428077Z" + } + }, + "outputs": [], + "source": [ + "\n", + "geom = deepxde.geometry.Interval(0, 1).to_dict_point(x=unit_of_x)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the boundary conditions for the problem." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T14:02:06.444358Z", + "start_time": "2024-12-17T14:02:06.439478Z" + } + }, + "outputs": [], + "source": [ + "\n", + "def boundary_l(x, on_boundary):\n", + " return u.math.logical_and(on_boundary, deepxde.utils.isclose(x['x'] / unit_of_x, 0))\n", + "\n", + "\n", + "def boundary_r(x, on_boundary):\n", + " return u.math.logical_and(on_boundary, deepxde.utils.isclose(x['x'] / unit_of_x, 1))\n", + "\n", + "\n", + "bc1 = deepxde.icbc.DirichletBC(lambda x: {'y': 0 * unit_of_u}, boundary_l)\n", + "bc2 = deepxde.icbc.NeumannBC(lambda x: {'y': 0 * unit_of_u}, boundary_l)\n", + "bc3 = deepxde.icbc.OperatorBC(lambda x, y: net.hessian(x)['y']['x']['x'] / u.meter, boundary_r)\n", + "bc4 = deepxde.icbc.OperatorBC(lambda x, y: net.gradient(x, order=3)['y']['x']['x']['x'] / u.meter ** 2, boundary_r)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the neural network model for the problem." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T14:02:06.903923Z", + "start_time": "2024-12-17T14:02:06.458887Z" + } + }, + "outputs": [], + "source": [ + "net = deepxde.nn.Model(\n", + " deepxde.nn.DictToArray(x=unit_of_x),\n", + " deepxde.nn.FNN([1] + [20] * 3 + [1], \"tanh\"),\n", + " deepxde.nn.ArrayToDict(y=unit_of_u),\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the exact solution for the problem." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T14:02:07.977054Z", + "start_time": "2024-12-17T14:02:06.913042Z" + } + }, + "outputs": [], + "source": [ + "def func(x):\n", + " x = x['x'] / unit_of_x\n", + " y = -(x ** 4) / 24 + x ** 3 / 6 - x ** 2 / 4\n", + " return {'y': y * unit_of_u}\n", + "\n", + "\n", + "data = deepxde.problem.PDE(\n", + " geom,\n", + " pde,\n", + " [bc1, bc2, bc3, bc4],\n", + " net,\n", + " num_domain=100,\n", + " num_boundary=20,\n", + " solution=func,\n", + " num_test=100,\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Train the model and evaluate the results." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T14:02:36.927956Z", + "start_time": "2024-12-17T14:02:08.206744Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Compiling trainer...\n", + "'compile' took 0.058168 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "0 [172697.52 * kilogram ** 2 * second ** -4, [198196.31 * kilogram ** 2 * second ** -4, [{'y': Array(0.49183828, dtype=float32)}] \n", + " {'ibc0': {'y': 0. * meter}}, {'ibc0': {'y': 0. * meter}}, \n", + " {'ibc1': {'y': 0.34124637 * meter}}, {'ibc1': {'y': 0.34124637 * meter}}, \n", + " {'ibc2': 0.02639124 * metre ** -2}, {'ibc2': 0.02639124 * metre ** -2}, \n", + " {'ibc3': 1.2099838 * metre ** -4}] {'ibc3': 1.2099838 * metre ** -4}] \n", + "1000 [8.933943 * kilogram ** 2 * second ** -4, [10.233379 * kilogram ** 2 * second ** -4, [{'y': Array(1.6421293, dtype=float32)}] \n", + " {'ibc0': {'y': 9.626521e-11 * meter}}, {'ibc0': {'y': 9.626521e-11 * meter}}, \n", + " {'ibc1': {'y': 0.17711917 * meter}}, {'ibc1': {'y': 0.17711917 * meter}}, \n", + " {'ibc2': 0.03371554 * metre ** -2}, {'ibc2': 0.03371554 * metre ** -2}, \n", + " {'ibc3': 0.3698493 * metre ** -4}] {'ibc3': 0.3698493 * metre ** -4}] \n", + "2000 [5.0301304 * kilogram ** 2 * second ** -4, [5.7454376 * kilogram ** 2 * second ** -4, [{'y': Array(1.2512381, dtype=float32)}] \n", + " {'ibc0': {'y': 5.3002607e-12 * meter}}, {'ibc0': {'y': 5.3002607e-12 * meter}}, \n", + " {'ibc1': {'y': 0.12062849 * meter}}, {'ibc1': {'y': 0.12062849 * meter}}, \n", + " {'ibc2': 0.02302191 * metre ** -2}, {'ibc2': 0.02302191 * metre ** -2}, \n", + " {'ibc3': 0.1910549 * metre ** -4}] {'ibc3': 0.1910549 * metre ** -4}] \n", + "3000 [2.1895514 * kilogram ** 2 * second ** -4, [2.4801166 * kilogram ** 2 * second ** -4, [{'y': Array(0.97356707, dtype=float32)}] \n", + " {'ibc0': {'y': 1.2275463e-11 * meter}}, {'ibc0': {'y': 1.2275463e-11 * meter}}, \n", + " {'ibc1': {'y': 0.08320159 * meter}}, {'ibc1': {'y': 0.08320159 * meter}}, \n", + " {'ibc2': 0.0165317 * metre ** -2}, {'ibc2': 0.0165317 * metre ** -2}, \n", + " {'ibc3': 0.08161929 * metre ** -4}] {'ibc3': 0.08161929 * metre ** -4}] \n", + "4000 [0.72300434 * kilogram ** 2 * second ** -4, [0.8063759 * kilogram ** 2 * second ** -4, [{'y': Array(0.8491821, dtype=float32)}] \n", + " {'ibc0': {'y': 8.0052675e-12 * meter}}, {'ibc0': {'y': 8.0052675e-12 * meter}}, \n", + " {'ibc1': {'y': 0.06257136 * meter}}, {'ibc1': {'y': 0.06257136 * meter}}, \n", + " {'ibc2': 0.01523586 * metre ** -2}, {'ibc2': 0.01523586 * metre ** -2}, \n", + " {'ibc3': 0.03002642 * metre ** -4}] {'ibc3': 0.03002642 * metre ** -4}] \n", + "5000 [0.30583796 * kilogram ** 2 * second ** -4, [0.3329344 * kilogram ** 2 * second ** -4, [{'y': Array(0.89385283, dtype=float32)}] \n", + " {'ibc0': {'y': 4.751356e-12 * meter}}, {'ibc0': {'y': 4.751356e-12 * meter}}, \n", + " {'ibc1': {'y': 0.05717417 * meter}}, {'ibc1': {'y': 0.05717417 * meter}}, \n", + " {'ibc2': 0.01894331 * metre ** -2}, {'ibc2': 0.01894331 * metre ** -2}, \n", + " {'ibc3': 0.01662517 * metre ** -4}] {'ibc3': 0.01662517 * metre ** -4}] \n", + "6000 [0.25211135 * kilogram ** 2 * second ** -4, [0.24109833 * kilogram ** 2 * second ** -4, [{'y': Array(0.9684854, dtype=float32)}] \n", + " {'ibc0': {'y': 6.294266e-10 * meter}}, {'ibc0': {'y': 6.294266e-10 * meter}}, \n", + " {'ibc1': {'y': 0.05709113 * meter}}, {'ibc1': {'y': 0.05709113 * meter}}, \n", + " {'ibc2': 0.02338268 * metre ** -2}, {'ibc2': 0.02338268 * metre ** -2}, \n", + " {'ibc3': 0.01612406 * metre ** -4}] {'ibc3': 0.01612406 * metre ** -4}] \n", + "7000 [0.88259137 * kilogram ** 2 * second ** -4, [0.624831 * kilogram ** 2 * second ** -4, [{'y': Array(0.99016815, dtype=float32)}] \n", + " {'ibc0': {'y': 6.6010295e-09 * meter}}, {'ibc0': {'y': 6.6010295e-09 * meter}}, \n", + " {'ibc1': {'y': 0.05649563 * meter}}, {'ibc1': {'y': 0.05649563 * meter}}, \n", + " {'ibc2': 0.02561221 * metre ** -2}, {'ibc2': 0.02561221 * metre ** -2}, \n", + " {'ibc3': 0.01722029 * metre ** -4}] {'ibc3': 0.01722029 * metre ** -4}] \n", + "8000 [0.21604834 * kilogram ** 2 * second ** -4, [0.19982578 * kilogram ** 2 * second ** -4, [{'y': Array(0.98142815, dtype=float32)}] \n", + " {'ibc0': {'y': 1.7951907e-10 * meter}}, {'ibc0': {'y': 1.7951907e-10 * meter}}, \n", + " {'ibc1': {'y': 0.05653544 * meter}}, {'ibc1': {'y': 0.05653544 * meter}}, \n", + " {'ibc2': 0.02618827 * metre ** -2}, {'ibc2': 0.02618827 * metre ** -2}, \n", + " {'ibc3': 0.01875774 * metre ** -4}] {'ibc3': 0.01875774 * metre ** -4}] \n", + "9000 [0.10451799 * kilogram ** 2 * second ** -4, [0.10789017 * kilogram ** 2 * second ** -4, [{'y': Array(0.93547827, dtype=float32)}] \n", + " {'ibc0': {'y': 4.1144904e-12 * meter}}, {'ibc0': {'y': 4.1144904e-12 * meter}}, \n", + " {'ibc1': {'y': 0.05326409 * meter}}, {'ibc1': {'y': 0.05326409 * meter}}, \n", + " {'ibc2': 0.02588784 * metre ** -2}, {'ibc2': 0.02588784 * metre ** -2}, \n", + " {'ibc3': 0.02023843 * metre ** -4}] {'ibc3': 0.02023843 * metre ** -4}] \n", + "10000 [0.09200532 * kilogram ** 2 * second ** -4, [0.09282021 * kilogram ** 2 * second ** -4, [{'y': Array(0.8544506, dtype=float32)}] \n", + " {'ibc0': {'y': 1.0899624e-12 * meter}}, {'ibc0': {'y': 1.0899624e-12 * meter}}, \n", + " {'ibc1': {'y': 0.04875687 * meter}}, {'ibc1': {'y': 0.04875687 * meter}}, \n", + " {'ibc2': 0.0242439 * metre ** -2}, {'ibc2': 0.0242439 * metre ** -2}, \n", + " {'ibc3': 0.02106431 * metre ** -4}] {'ibc3': 0.02106431 * metre ** -4}] \n", + "\n", + "Best trainer at step 10000:\n", + " train loss: 1.86e-01\n", + " test loss: 1.87e-01\n", + " test metric: [{'y': Array(0.85, dtype=float32)}]\n", + "\n", + "'train' took 27.923877 s\n", + "\n", + "Saving loss history to D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\loss.dat ...\n", + "Saving checkpoint into D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\loss.dat\n", + "Saving training data to D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\train.dat ...\n", + "Saving checkpoint into D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\train.dat\n", + "Saving test data to D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\test.dat ...\n", + "Saving checkpoint into D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\test.dat\n" + ] + }, + { + "data": { + "image/png": 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", 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "trainer = deepxde.Trainer(data)\n", + "trainer.compile(bst.optim.Adam(0.001), metrics=[\"l2 relative error\"]).train(iterations=10000)\n", + "trainer.saveplot(issave=True, isplot=True)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/docs/experimental_docs/unit-examples-forward/Euler_beam.py b/docs/experimental_docs/unit-examples-forward/Euler_beam.py new file mode 100644 index 000000000..111ddce50 --- /dev/null +++ b/docs/experimental_docs/unit-examples-forward/Euler_beam.py @@ -0,0 +1,63 @@ +import brainstate as bst +import brainunit as u + +import deepxde.experimental as deepxde + +unit_of_u = u.meter +unit_of_x = u.meter +unit_of_E = u.pascal +unit_of_I = u.meter ** 4 +unit_of_p = u.kilogram / u.second ** 2 + +geom = deepxde.geometry.Interval(0, 1).to_dict_point(x=unit_of_x) + +E = 1 * unit_of_E +I = 1 * unit_of_I +p = -1. * unit_of_p + + +def pde(x, y): + dy_xxxx = net.gradient(x, order=4)['y']['x']['x']['x']['x'] + return E * I * dy_xxxx - p + + +def boundary_l(x, on_boundary): + return u.math.logical_and(on_boundary, deepxde.utils.isclose(x['x'] / unit_of_x, 0)) + + +def boundary_r(x, on_boundary): + return u.math.logical_and(on_boundary, deepxde.utils.isclose(x['x'] / unit_of_x, 1)) + + +bc1 = deepxde.icbc.DirichletBC(lambda x: {'y': 0 * unit_of_u}, boundary_l) +bc2 = deepxde.icbc.NeumannBC(lambda x: {'y': 0 * unit_of_u}, boundary_l) +bc3 = deepxde.icbc.OperatorBC(lambda x, y: net.hessian(x)['y']['x']['x'] / u.meter, boundary_r) +bc4 = deepxde.icbc.OperatorBC(lambda x, y: net.gradient(x, order=3)['y']['x']['x']['x'] / u.meter ** 2, boundary_r) + +net = deepxde.nn.Model( + deepxde.nn.DictToArray(x=unit_of_x), + deepxde.nn.FNN([1] + [20] * 3 + [1], "tanh"), + deepxde.nn.ArrayToDict(y=unit_of_u), +) + + +def func(x): + x = x['x'] / unit_of_x + y = -(x ** 4) / 24 + x ** 3 / 6 - x ** 2 / 4 + return {'y': y * unit_of_u} + + +data = deepxde.problem.PDE( + geom, + pde, + [bc1, bc2, bc3, bc4], + net, + num_domain=100, + num_boundary=20, + solution=func, + num_test=100, +) + +trainer = deepxde.Trainer(data) +trainer.compile(bst.optim.Adam(0.001), metrics=["l2 relative error"]).train(iterations=10000) +trainer.saveplot(issave=True, isplot=True) diff --git a/docs/experimental_docs/unit-examples-forward/Helmholtz_Dirichlet_2d.ipynb b/docs/experimental_docs/unit-examples-forward/Helmholtz_Dirichlet_2d.ipynb new file mode 100644 index 000000000..ac1491782 --- /dev/null +++ b/docs/experimental_docs/unit-examples-forward/Helmholtz_Dirichlet_2d.ipynb @@ -0,0 +1,356 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Helmholtz equation over a 2D square domain\n", + "\n", + "## Problem setup\n", + "For a wave number $k_0 = 2\\pi n$ with $n = 2$, we will solve a Helmholtz equation:\n", + "\n", + "$$\n", + "- u_{xx}-u_{yy} - k_0^2 u = f, \\qquad \\Omega = [0,1]^2\n", + "$$\n", + "\n", + "with the Dirichlet boundary conditions\n", + "\n", + "$$\n", + "u(x,y)=0, \\qquad (x,y)\\in \\partial \\Omega\n", + "$$\n", + "\n", + "and a source term $f(x,y) = k_0^2 \\sin(k_0 x)\\sin(k_0 y)$.\n", + "\n", + "Remark that the exact solution reads:\n", + "$$\n", + "u(x,y)= \\sin(k_0 x)\\sin(k_0 y)\n", + "$$\n", + "\n", + "\n", + "## Dimensional Analysis\n", + "\n", + "### **Assigning Physical Units:**\n", + "\n", + "To perform dimensional analysis, we will assign physical units to each variable and parameter in the equation. We'll ensure that both sides of the Helmholtz equation have consistent dimensions.\n", + "\n", + "#### **Variables and Parameters:**\n", + "\n", + "| **Variable/Parameter** | **Symbol** | **Physical Quantity** | **Unit (SI)** | **Dimension** |\n", + "|------------------------|------------|-----------------------------------|---------------------------------------------------------------------------------|--------------------------|\n", + "| **Field Variable** | $ u $ | Scalar field (e.g., displacement, pressure) | **Dimensionless** or [U] [Depends on Physical Context] | $[U]$ |\n", + "| **Spatial Coordinate** | $ x, y $ | Position in space | meters (m) | Length $[L]$ |\n", + "| **Wave Number** | $ k_0 $ | Spatial frequency | inverse meters (1/m) | $[L]^{-1}$ |\n", + "| **Source Term** | $ f $ | External forcing or source | Depends on $ u $'s units (e.g., if $ u $ is dimensionless, f has units of 1/m²) | $[U][L]^{-2}$ |\n", + "\n", + "> **Note:** The units of $ u $ can vary based on the physical context of the problem. However, based on the exact solution provided, $ u(x,y) = \\sin(k_0 x) \\sin(k_0 y) $, it suggests that $ u $ is **dimensionless**. Therefore, for this analysis, we'll assume $ u $ is dimensionless.\n", + "\n", + "#### **Detailed Assignments:**\n", + "\n", + "1. **Field Variable ($ u $):**\n", + " - **Physical Quantity:** Scalar field (e.g., displacement, pressure)\n", + " - **Unit:** **Dimensionless**\n", + " - **Dimension:** $[1]$\n", + " \n", + "2. **Spatial Coordinates ($ x, y $):**\n", + " - **Physical Quantity:** Position in space\n", + " - **Unit:** meters (m)\n", + " - **Dimension:** Length $[L]$\n", + " \n", + "3. **Wave Number ($ k_0 $):**\n", + " - **Physical Quantity:** Spatial frequency\n", + " - **Unit:** inverse meters (1/m)\n", + " - **Dimension:** $[L]^{-1}$\n", + " \n", + "4. **Source Term ($ f $):**\n", + " - **Physical Quantity:** External forcing or source\n", + " - **Unit:** inverse meters squared (1/m²)\n", + " - **Dimension:** $[L]^{-2}$\n", + " \n", + "#### **Dimensional Consistency Check:**\n", + "\n", + "To ensure the Helmholtz equation is dimensionally consistent, both sides of the equation must have the same dimensions.\n", + "\n", + "1. **Left Side ($ -u_{xx} - u_{yy} - k_0^2 u $):**\n", + " - $ u_{xx} = \\frac{\\partial^2 u}{\\partial x^2} $: \n", + " - Dimension: $\\frac{[U]}{[L]^2}$ \n", + " - Since $ u $ is dimensionless: $[U] = 1$, so $ u_{xx} $ has dimension $[L]^{-2}$.\n", + " \n", + " - $ u_{yy} = \\frac{\\partial^2 u}{\\partial y^2} $:\n", + " - Dimension: Same as $ u_{xx} $, i.e., $[L]^{-2}$.\n", + " \n", + " - $ k_0^2 u $:\n", + " - Dimension: $[k_0]^2 [U] = [L]^{-2} \\times 1 = [L]^{-2}$.\n", + " \n", + " - **Combined Left Side:** Each term has dimension $[L]^{-2}$, ensuring consistency.\n", + " \n", + "2. **Right Side ($ f $):**\n", + " - Dimension: $[L]^{-2}$.\n", + " \n", + " - **Conclusion:** Both sides of the equation have the same dimension $[L]^{-2}$, confirming dimensional consistency.\n", + "\n", + "### **Summary of Physical Units:**\n", + "\n", + "| **Symbol** | **Physical Quantity** | **Unit (SI)** | **Dimension** |\n", + "|------------|-------------------------------------------|---------------------|--------------------------|\n", + "| $ u $ | Scalar field (dimensionless) | Dimensionless | $[1]$ |\n", + "| $ x, y $ | Spatial coordinates | meters (m) | Length $[L]$ |\n", + "| $ k_0 $ | Wave number | inverse meters (1/m)| $[L]^{-1}$ |\n", + "| $ f $ | Source term | inverse meters squared (1/m²)| $[L]^{-2}$ |\n", + "\n", + "### **Boundary Conditions Units:**\n", + "\n", + "1. **Dirichlet Boundary Conditions ($ u(x,y) = 0 $):**\n", + " - **Units:** Same as $ u $, which is **dimensionless**.\n", + " \n", + "2. **Exact Solution ($ u(x,y) = \\sin(k_0 x) \\sin(k_0 y) $):**\n", + " - **Units:** Dimensionless, consistent with $ u $'s units.\n", + "\n", + "### **Conclusion:**\n", + "\n", + "All variables and parameters in the Helmholtz equation have been assigned consistent physical units, ensuring the dimensional integrity of the equation and its boundary conditions. Specifically:\n", + "\n", + "- **$ u $** is dimensionless.\n", + "- **$ x $** and **$ y $** are measured in meters (m).\n", + "- **$ k_0 $** has units of inverse meters (1/m).\n", + "- **$ f $** has units of inverse meters squared (1/m²).\n", + "\n", + "This dimensional assignment ensures that the Helmholtz equation is dimensionally consistent and the boundary conditions are appropriately defined.\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code Implementation\n", + "\n", + "First, import the necessary libraries and modules for the problem setup and solution:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T14:18:10.846957Z", + "start_time": "2024-12-17T14:18:07.057723Z" + } + }, + "outputs": [], + "source": [ + "import brainstate as bst\n", + "import brainunit as u\n", + "import numpy as np\n", + "\n", + "import deepxde.experimental as deepxde" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the physical units and parameters for the Helmholtz equation:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T14:18:10.855991Z", + "start_time": "2024-12-17T14:18:10.850982Z" + } + }, + "outputs": [], + "source": [ + "unit_of_u = u.UNITLESS\n", + "unit_of_x = u.meter\n", + "unit_of_y = u.meter\n", + "unit_of_k0 = 1 / unit_of_x\n", + "unit_of_f = 1 / u.meter ** 2\n", + "\n", + "# General parameters\n", + "n = 2\n", + "precision_train = 10\n", + "precision_test = 30\n", + "hard_constraint = True # True or False\n", + "weights = 100 # if hard_constraint == False\n", + "iterations = 5000\n", + "parameters = [1e-3, 3, 150]\n", + "\n", + "learning_rate, num_dense_layers, num_dense_nodes = parameters\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the PDE function for the Helmholtz equation:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T14:18:10.873024Z", + "start_time": "2024-12-17T14:18:10.867395Z" + } + }, + "outputs": [], + "source": [ + "geom = deepxde.geometry.Rectangle([0, 0], [1, 1]).to_dict_point(x=unit_of_x, y=unit_of_y)\n", + "k0 = 2 * np.pi * n\n", + "wave_len = 1 / n\n", + "\n", + "hx_train = wave_len / precision_train\n", + "nx_train = int(1 / hx_train)\n", + "\n", + "hx_test = wave_len / precision_test\n", + "nx_test = int(1 / hx_test)\n", + "\n", + "\n", + "def pde(x, y):\n", + " hessian = net.hessian(x)\n", + "\n", + " dy_xx = hessian[\"y\"][\"x\"][\"x\"]\n", + " dy_yy = hessian[\"y\"][\"y\"][\"y\"]\n", + "\n", + " f = k0 ** 2 * u.math.sin(k0 * x['x'] / unit_of_x) * u.math.sin(k0 * x['y'] / unit_of_y)\n", + " return -dy_xx - dy_yy - (k0 * unit_of_k0) ** 2 * y['y'] - f * unit_of_f\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the boundary conditions for the Helmholtz equation:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T14:18:11.385027Z", + "start_time": "2024-12-17T14:18:10.883839Z" + } + }, + "outputs": [], + "source": [ + "\n", + "\n", + "if hard_constraint:\n", + " bc = []\n", + "else:\n", + " bc = deepxde.icbc.DirichletBC(lambda x: {'y': 0 * unit_of_u})\n", + "\n", + "net = deepxde.nn.Model(\n", + " deepxde.nn.DictToArray(x=unit_of_x, y=unit_of_y),\n", + " deepxde.nn.FNN([2] + [num_dense_nodes] * num_dense_layers + [1],\n", + " u.math.sin,\n", + " bst.init.KaimingUniform()),\n", + " deepxde.nn.ArrayToDict(y=unit_of_u),\n", + ")\n", + "\n", + "if hard_constraint:\n", + " def transform(x, y):\n", + " x = deepxde.utils.array_to_dict(x, [\"x\", \"y\"], keep_dim=True)\n", + " res = x['x'] * (1 - x['x']) * x['y'] * (1 - x['y'])\n", + " return res * y\n", + "\n", + "\n", + " net.approx.apply_output_transform(transform)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the problem and train the model to solve the Helmholtz equation:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T14:18:11.811162Z", + "start_time": "2024-12-17T14:18:11.398719Z" + } + }, + "outputs": [], + "source": [ + "problem = deepxde.problem.PDE(\n", + " geom,\n", + " pde,\n", + " bc,\n", + " net,\n", + " num_domain=nx_train ** 2,\n", + " num_boundary=4 * nx_train,\n", + " solution=lambda x: {'y': u.math.sin(k0 * x['x'] / unit_of_x) * u.math.sin(k0 * x['y'] / unit_of_y) * unit_of_u},\n", + " num_test=nx_test ** 2,\n", + " loss_weights=None if hard_constraint else [1, weights],\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Train the model using the Adam optimizer and the specified learning rate:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T14:19:14.913372200Z", + "start_time": "2024-12-17T14:18:11.822636Z" + }, + "jupyter": { + "is_executing": true + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Compiling trainer...\n", + "'compile' took 0.059387 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "0 [5213.1675 * metre ** -4] [6450.17 * metre ** -4] [{'y': Array(1.0007389, dtype=float32)}] \n", + "1000 [115.11537 * metre ** -4] [164.17776 * metre ** -4] [{'y': Array(0.50004345, dtype=float32)}] \n" + ] + } + ], + "source": [ + "trainer = deepxde.Trainer(problem)\n", + "trainer.compile(bst.optim.Adam(learning_rate), metrics=[\"l2 relative error\"]).train(iterations=iterations)\n", + "trainer.saveplot(issave=True, isplot=True)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "pinnx", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python", + "version": "3.10.15" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/docs/experimental_docs/unit-examples-forward/Helmholtz_Dirichlet_2d.py b/docs/experimental_docs/unit-examples-forward/Helmholtz_Dirichlet_2d.py new file mode 100644 index 000000000..ca7ab60a2 --- /dev/null +++ b/docs/experimental_docs/unit-examples-forward/Helmholtz_Dirichlet_2d.py @@ -0,0 +1,81 @@ +import brainstate as bst +import brainunit as u +import numpy as np + +import deepxde.experimental as deepxde + +unit_of_u = u.UNITLESS +unit_of_x = u.meter +unit_of_y = u.meter +unit_of_k0 = 1 / unit_of_x +unit_of_f = 1 / u.meter ** 2 + +# General parameters +n = 2 +precision_train = 10 +precision_test = 30 +hard_constraint = True # True or False +weights = 100 # if hard_constraint == False +iterations = 5000 +parameters = [1e-3, 3, 150] + +learning_rate, num_dense_layers, num_dense_nodes = parameters + +geom = deepxde.geometry.Rectangle([0, 0], [1, 1]).to_dict_point(x=unit_of_x, y=unit_of_y) +k0 = 2 * np.pi * n +wave_len = 1 / n + +hx_train = wave_len / precision_train +nx_train = int(1 / hx_train) + +hx_test = wave_len / precision_test +nx_test = int(1 / hx_test) + +def pde(x, y): + hessian = net.hessian(x) + + dy_xx = hessian["y"]["x"]["x"] + dy_yy = hessian["y"]["y"]["y"] + + f = k0 ** 2 * u.math.sin(k0 * x['x'] / unit_of_x) * u.math.sin(k0 * x['y'] / unit_of_y) + return -dy_xx - dy_yy - (k0 * unit_of_k0) ** 2 * y['y'] - f * unit_of_f + + + +if hard_constraint: + bc = [] +else: + bc = deepxde.icbc.DirichletBC(lambda x: {'y': 0 * unit_of_u}) + +net = deepxde.nn.Model( + deepxde.nn.DictToArray(x=unit_of_x, y=unit_of_y), + deepxde.nn.FNN([2] + [num_dense_nodes] * num_dense_layers + [1], + u.math.sin, + bst.init.KaimingUniform()), + deepxde.nn.ArrayToDict(y=unit_of_u), +) + +if hard_constraint: + def transform(x, y): + x = deepxde.utils.array_to_dict(x, ["x", "y"], keep_dim=True) + res = x['x'] * (1 - x['x']) * x['y'] * (1 - x['y']) + return res * y + + + net.approx.apply_output_transform(transform) + +problem = deepxde.problem.PDE( + geom, + pde, + bc, + net, + num_domain=nx_train ** 2, + num_boundary=4 * nx_train, + solution=lambda x: {'y': u.math.sin(k0 * x['x'] / unit_of_x) * u.math.sin(k0 * x['y'] / unit_of_y) * unit_of_u}, + num_test=nx_test ** 2, + loss_weights=None if hard_constraint else [1, weights], +) + +trainer = deepxde.Trainer(problem) +trainer.compile(bst.optim.Adam(learning_rate), metrics=["l2 relative error"]).train(iterations=iterations) +trainer.saveplot(issave=True, isplot=True) diff --git a/docs/experimental_docs/unit-examples-forward/Laplace_disk.ipynb b/docs/experimental_docs/unit-examples-forward/Laplace_disk.ipynb new file mode 100644 index 000000000..ca2547cf5 --- /dev/null +++ b/docs/experimental_docs/unit-examples-forward/Laplace_disk.ipynb @@ -0,0 +1,535 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Laplace equation on a disk\n", + "## Problem setup\n", + "We will solve a Laplace equation in a polar coordinate system:\n", + "\n", + "$$\n", + "r\\frac{dy}{dr} + r^2\\frac{dy^2}{dr^2} + \\frac{dy^2}{d\\theta^2} = 0, \\qquad r \\in [0, 1], \\quad \\theta \\in [0, 2\\pi]\n", + "$$\n", + "\n", + "with the Dirichlet boundary condition\n", + "\n", + "$$\n", + "y(1,\\theta) = \\cos(\\theta)\n", + "$$\n", + "\n", + "and the periodic boundary condition\n", + "\n", + "$$\n", + "y(r, \\theta +2\\pi) = y(r, \\theta).\n", + "$$\n", + "\n", + "The reference solution is $y=r\\cos(\\theta)$.\n", + "\n", + "# Dimensional Analysis for the Laplace Equation on a Disk\n", + "\n", + "## Problem Setup\n", + "\n", + "We will solve the Laplace equation in a polar coordinate system:\n", + "\n", + "$$\n", + "r\\frac{dy}{dr} + r^2\\frac{d^2y}{dr^2} + \\frac{d^2y}{d\\theta^2} = 0, \\qquad r \\in [0, 1], \\quad \\theta \\in [0, 2\\pi]\n", + "$$\n", + "\n", + "with the Dirichlet boundary condition:\n", + "\n", + "$$\n", + "y(1,\\theta) = \\cos(\\theta)\n", + "$$\n", + "\n", + "and the periodic boundary condition:\n", + "\n", + "$$\n", + "y(r, \\theta + 2\\pi) = y(r, \\theta).\n", + "$$\n", + "\n", + "The reference solution is:\n", + "\n", + "$$\n", + "y = r\\cos(\\theta).\n", + "$$\n", + "\n", + "---\n", + "\n", + "## Dimensional Analysis\n", + "\n", + "### Step 1: Assign Dimensions to Variables\n", + "\n", + "1. **Radial Coordinate $r$:**\n", + " - The dimension of $r$ is length:\n", + "\n", + " $$\n", + " [r] = L.\n", + " $$\n", + "\n", + "2. **Angular Coordinate $\\theta$:**\n", + " - The dimension of $\\theta$ is dimensionless:\n", + "\n", + " $$\n", + " [\\theta] = 1.\n", + " $$\n", + "\n", + "3. **Solution $y$:**\n", + " - The solution $y$ represents a physical quantity, which we assume to be in volts (V):\n", + "\n", + " $$\n", + " [y] = V.\n", + " $$\n", + "\n", + "---\n", + "\n", + "### Step 2: Analyze the Dimensions of Each Term\n", + "\n", + "1. **First Derivative Term $r\\frac{dy}{dr}$:**\n", + " - The first derivative $\\frac{dy}{dr}$ has dimensions:\n", + "\n", + " $$\n", + " \\left[\\frac{dy}{dr}\\right] = \\frac{[y]}{[r]} = \\frac{V}{L}.\n", + " $$\n", + " - Therefore, the term $r\\frac{dy}{dr}$ has dimensions:\n", + "\n", + " $$\n", + " \\left[r\\frac{dy}{dr}\\right] = [r] \\cdot \\frac{V}{L} = L \\cdot \\frac{V}{L} = V.\n", + " $$\n", + "\n", + "2. **Second Derivative Term $r^2\\frac{d^2y}{dr^2}$:**\n", + " - The second derivative $\\frac{d^2y}{dr^2}$ has dimensions:\n", + "\n", + " $$\n", + " \\left[\\frac{d^2y}{dr^2}\\right] = \\frac{[y]}{[r]^2} = \\frac{V}{L^2}.\n", + " $$\n", + " - Therefore, the term $r^2\\frac{d^2y}{dr^2}$ has dimensions:\n", + "\n", + " $$\n", + " \\left[r^2\\frac{d^2y}{dr^2}\\right] = [r]^2 \\cdot \\frac{V}{L^2} = L^2 \\cdot \\frac{V}{L^2} = V.\n", + " $$\n", + "\n", + "3. **Second Derivative Term $\\frac{d^2y}{d\\theta^2}$:**\n", + " - The second derivative $\\frac{d^2y}{d\\theta^2}$ has dimensions:\n", + "\n", + " $$\n", + " \\left[\\frac{d^2y}{d\\theta^2}\\right] = \\frac{[y]}{[\\theta]^2} = \\frac{V}{1^2} = V.\n", + " $$\n", + "\n", + "---\n", + "\n", + "### Step 3: Verify Dimensional Consistency\n", + "\n", + "The Laplace equation in polar coordinates is:\n", + "\n", + "$$\n", + "r\\frac{dy}{dr} + r^2\\frac{d^2y}{dr^2} + \\frac{d^2y}{d\\theta^2} = 0.\n", + "$$\n", + "\n", + "Each term in the equation has dimensions of $V$:\n", + "\n", + "- $r\\frac{dy}{dr}$: $V$\n", + "- $r^2\\frac{d^2y}{dr^2}$: $V$\n", + "- $\\frac{d^2y}{d\\theta^2}$: $V$\n", + "\n", + "Since all terms have the same dimensions, the equation is dimensionally consistent.\n", + "\n", + "---\n", + "\n", + "### Step 4: Summary of Dimensions\n", + "\n", + "| Variable/Parameter | Physical Meaning | Dimensions |\n", + "|------------------------|-----------------------------------|-----------------------|\n", + "| $r$ | Radial coordinate | $L$ |\n", + "| $\\theta$ | Angular coordinate | $1$ (dimensionless) |\n", + "| $y$ | Solution (e.g., voltage) | $V$ |\n", + "\n", + "---\n", + "\n", + "### Step 5: Initial and Boundary Conditions\n", + "\n", + "1. **Boundary Condition $y(1,\\theta) = \\cos(\\theta)$:**\n", + " - The boundary condition $y(1,\\theta) = \\cos(\\theta)$ is given in volts:\n", + " \n", + " $$\n", + " [y(1,\\theta)] = V.\n", + " $$\n", + " - The term $\\cos(\\theta)$ is dimensionless because $\\theta$ is dimensionless.\n", + "\n", + "2. **Periodic Boundary Condition $y(r, \\theta + 2\\pi) = y(r, \\theta)$:**\n", + " - The periodic boundary condition ensures that the solution is periodic in $\\theta$ with period $2\\pi$.\n", + " - Since $\\theta$ is dimensionless, the condition is dimensionally consistent.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Implementation\n", + "This description goes through the implementation of a solver for the above described Heat equation step-by-step.\n", + "\n", + "First, import the libraries we need:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import brainstate as bst\n", + "import brainunit as u\n", + "import numpy as np\n", + "\n", + "import deepxde.experimental as deepxde" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We begin by defining a computational geometry. We can use a built-in class `Rectangle` as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "geom = deepxde.geometry.Rectangle(\n", + " xmin=[0, 0],\n", + " xmax=[1, 2 * np.pi],\n", + ").to_dict_point(r=u.meter, theta=u.radian)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we express the PDE residual of the Laplace equation:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def pde(x, y):\n", + " jacobian = net.jacobian(x)\n", + " hessian = net.hessian(x)\n", + "\n", + " dy_r = jacobian[\"y\"][\"r\"]\n", + " dy_rr = hessian[\"y\"][\"r\"][\"r\"]\n", + " dy_thetatheta = hessian[\"y\"][\"theta\"][\"theta\"]\n", + " return x['r'] * dy_r + x['r'] ** 2 * dy_rr + dy_thetatheta" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first argument to `pde` is 2-dimensional vector where the first component(`x[:,0:1]`) is $r$-coordinate and the second componenet (`x[:,1:]`) is the $\\theta$-coordinate. The second argument is the network output, i.e., the solution $y(r, \\theta)$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we consider the Dirichlet boundary condition. We need to implement a function, which should return `True` for points inside the subdomain and `False` for the points outside. In our case, if the points satisfy $r=1$ and are on the whole boundary of the rectangle domain, then function `boundary` returns `True`. Otherwise, it returns `False`. (Note that because of rounding-off errors, it is often wise to use u.math.allclose to test whether two floating point values are equivalent.)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def boundary(x, on_boundary):\n", + " return on_boundary and u.math.allclose(x['r'], 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The argument `x` to `boundary` is the network input and is a $d$-dim vector, where $d$ is the dimension and $d=2$ in this case. To facilitate the implementation of `boundary`, a boolean `on_boundary` is used as the second argument. If the point $r,\\theta$ (the first argument) is on the entire boundary of the rectangle geometry that created above, then `on_boundary` is `True`, otherwise, `on_boundary` is False." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using a lambda funtion, the `boundary` we defined above can be passed to `DirichletBC` as the second argument. Thus, the Dirichlet boundary condition is" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "uy = u.volt / u.meter\n", + "bc = deepxde.icbc.DirichletBC(\n", + " lambda x: {'y': u.math.cos(x['theta']) * uy},\n", + " lambda x, on_boundary: u.math.logical_and(on_boundary, u.math.allclose(x['r'], 1 * u.meter)),\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we rewrite this problem in cartesian coordinates, the variables are in the form of $[r\\sin(\\theta), r\\cos(\\theta)]$. We use them as features to satisfy the certain underlying physical constraints, so that the network is automatically periodic along the $\\theta$ coordinate and the period is $2\\pi$.\n", + "\n", + "Next, we choose the network. Here, we use a fully connected neural network of depth 4 (i.e., 3 hidden layers) and width 20:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# Use [r*sin(theta), r*cos(theta)] as features,\n", + "# so that the network is automatically periodic along the theta coordinate.\n", + "def feature_transform(x):\n", + " x = deepxde.utils.array_to_dict(x, [\"r\", \"theta\"], keep_dim=True)\n", + " return u.math.concatenate([x['r'] * u.math.sin(x['theta']),\n", + " x['r'] * u.math.cos(x['theta'])], axis=-1)\n", + "\n", + "net = deepxde.nn.Model(\n", + " deepxde.nn.DictToArray(r=u.meter, theta=u.radian),\n", + " deepxde.nn.FNN([2] + [20] * 3 + [1], \"tanh\", input_transform=feature_transform),\n", + " deepxde.nn.ArrayToDict(y=uy),\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, we have specified the geometry, PDE residual, and boundary condition. We then define the `PDE` problem as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The argument `solution` is the reference solution to compute the error of our solution, and we define it as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "def solution(x):\n", + " r, theta = x['r'], x['theta']\n", + " return {'y': r * u.math.cos(theta) * uy / u.meter}" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "problem = deepxde.problem.PDE(\n", + " geom,\n", + " pde,\n", + " bc,\n", + " net,\n", + " num_domain=2540,\n", + " num_boundary=80,\n", + " solution=solution\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, we have the PDE problem and the network. We bulid a `trainer` and choose the optimizer and learning rate:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Compiling trainer...\n", + "'compile' took 0.093740 s\n", + "\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trainer = deepxde.Trainer(problem)\n", + "trainer.compile(bst.optim.Adam(1e-3), metrics=[\"l2 relative error\"])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then train the model for 15000 iterations:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "0 [3.4136772 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [3.4136772 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [{'y': Array(1.9016247, dtype=float32)}] \n", + " {'ibc0': {'y': 1.2442183 * volt / meter}}] {'ibc0': {'y': 1.2442183 * volt / meter}}] \n", + "1000 [0.00209501 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [0.00209501 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [{'y': Array(0.03482116, dtype=float32)}] \n", + " {'ibc0': {'y': 9.6204014e-05 * volt / meter}}] {'ibc0': {'y': 9.6204014e-05 * volt / meter}}] \n", + "2000 [0.00059394 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [0.00059394 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [{'y': Array(0.02848322, dtype=float32)}] \n", + " {'ibc0': {'y': 1.8821578e-05 * volt / meter}}] {'ibc0': {'y': 1.8821578e-05 * volt / meter}}] \n", + "3000 [0.0003004 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [0.0003004 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [{'y': Array(0.01964555, dtype=float32)}] \n", + " {'ibc0': {'y': 1.1315266e-05 * volt / meter}}] {'ibc0': {'y': 1.1315266e-05 * volt / meter}}] \n", + "4000 [0.0001739 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [0.0001739 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [{'y': Array(0.0129396, dtype=float32)}] \n", + " {'ibc0': {'y': 8.526638e-06 * volt / meter}}] {'ibc0': {'y': 8.526638e-06 * volt / meter}}] \n", + "5000 [0.00010057 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [0.00010057 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [{'y': Array(0.00673189, dtype=float32)}] \n", + " {'ibc0': {'y': 6.3102784e-06 * volt / meter}}] {'ibc0': {'y': 6.3102784e-06 * volt / meter}}] \n", + "6000 [5.6971734e-05 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [5.6971734e-05 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [{'y': Array(0.00247048, dtype=float32)}] \n", + " {'ibc0': {'y': 4.33217e-06 * volt / meter}}] {'ibc0': {'y': 4.33217e-06 * volt / meter}}] \n", + "7000 [3.255158e-05 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [3.255158e-05 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [{'y': Array(0.0019735, dtype=float32)}] \n", + " {'ibc0': {'y': 2.83005e-06 * volt / meter}}] {'ibc0': {'y': 2.83005e-06 * volt / meter}}] \n", + "8000 [2.4938374e-05 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [2.4938374e-05 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [{'y': Array(0.00377944, dtype=float32)}] \n", + " {'ibc0': {'y': 4.333744e-06 * volt / meter}}] {'ibc0': {'y': 4.333744e-06 * volt / meter}}] \n", + "9000 [1.1950426e-05 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [1.1950426e-05 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [{'y': Array(0.00174527, dtype=float32)}] \n", + " {'ibc0': {'y': 1.2896384e-06 * volt / meter}}] {'ibc0': {'y': 1.2896384e-06 * volt / meter}}] \n", + "10000 [8.125793e-06 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [8.125793e-06 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [{'y': Array(0.00141424, dtype=float32)}] \n", + " {'ibc0': {'y': 9.607884e-07 * volt / meter}}] {'ibc0': {'y': 9.607884e-07 * volt / meter}}] \n", + "11000 [7.288996e-06 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [7.288996e-06 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [{'y': Array(0.00191965, dtype=float32)}] \n", + " {'ibc0': {'y': 1.3772864e-06 * volt / meter}}] {'ibc0': {'y': 1.3772864e-06 * volt / meter}}] \n", + "12000 [5.566375e-06 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [5.566375e-06 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [{'y': Array(0.00146894, dtype=float32)}] \n", + " {'ibc0': {'y': 9.980397e-07 * volt / meter}}] {'ibc0': {'y': 9.980397e-07 * volt / meter}}] \n", + "13000 [4.0166346e-06 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [4.0166346e-06 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [{'y': Array(0.00078307, dtype=float32)}] \n", + " {'ibc0': {'y': 4.9924233e-07 * volt / meter}}] {'ibc0': {'y': 4.9924233e-07 * volt / meter}}] \n", + "14000 [3.4733355e-06 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [3.4733355e-06 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [{'y': Array(0.00065782, dtype=float32)}] \n", + " {'ibc0': {'y': 4.2479667e-07 * volt / meter}}] {'ibc0': {'y': 4.2479667e-07 * volt / meter}}] \n", + "15000 [4.31375e-06 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [4.31375e-06 * 10.0^0 * (meter * (volt / meter) / meter) ** 2, [{'y': Array(0.0016097, dtype=float32)}] \n", + " {'ibc0': {'y': 1.0574405e-06 * volt / meter}}] {'ibc0': {'y': 1.0574405e-06 * volt / meter}}] \n", + "\n", + "Best trainer at step 14000:\n", + " train loss: 3.90e-06\n", + " test loss: 3.90e-06\n", + " test metric: [{'y': Array(0., dtype=float32)}]\n", + "\n", + "'train' took 56.701270 s\n", + "\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trainer.train(iterations=15000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We also save and plot the best trained result and loss history." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving loss history to /Users/sichaohe/Documents/GitHub/pinnx/docs/examples-pinn-forward/loss.dat ...\n", + "Saving checkpoint into /Users/sichaohe/Documents/GitHub/pinnx/docs/examples-pinn-forward/loss.dat\n", + "Saving training data to /Users/sichaohe/Documents/GitHub/pinnx/docs/examples-pinn-forward/train.dat ...\n", + "Saving checkpoint into /Users/sichaohe/Documents/GitHub/pinnx/docs/examples-pinn-forward/train.dat\n", + "Saving test data to /Users/sichaohe/Documents/GitHub/pinnx/docs/examples-pinn-forward/test.dat ...\n", + "Saving checkpoint into /Users/sichaohe/Documents/GitHub/pinnx/docs/examples-pinn-forward/test.dat\n" + ] + }, + { + "data": { + "image/png": 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", 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kXVt2eT1zIZPPIoeYvTUhBJvNhpCQEGRlZc3qHFINB+Pj42hoaEBSUhKKi4slN8zZtmv7eo2nC4QbLbetm6hRc9u61Wp1QJvmYot8iMWDLxDaR1itVjd7DTHClnJ5BWQyOt0gk88iBk3TcDqdPImcsbExNDU1ITk5GQUFBWhoaJj1eYQNBzRNo6OjA/39/SguLkZ6errH1/u7AZJ2cE93ymKvWSyRj7/vV6qtW6fTYXBwEDRNs2QUFxfnc1v3YiMff36fQoSFhXm1j+AqdhOvJymXVwDssDVR95ZdXhcXZPJZhBCb3aFpGm1tbRgeHsaKFSuQkpICo9E4J9EGN/KxWCyor6+H0+mUTLOJvR7wPfIZGhpCc3Mzr3byVbFIEGvr5gqA9vb2un0u4eHhop/LbDb7+YA/kY83CO0juGTkzT4CmPlsNBoNxsfHUVJSAgCyy+sig0w+iwxciRxg5g/GZDKhrq4OSqUSVVVVCA8PB+C9UcBXkMhnbGwMjY2NSElJwbJly/yqS/gSmbhcLrS2tmJ0dBQlJSUICgqCXq/H5OQkurq6EBQUxFOl5rYvL5bIZ66vQSgASjTXtFotT+ZGaB3Bff1iwXxFYmKEzfV6krKPAMBGPLLL6+KDTD6LCFzfHdLdMzQ0hNbWVmRlZaGgoIB3p+vvcKgnDA4OQqfTYfny5UhNTfX79d5mhYQEGhQUBJfLhejoaFZbjAwtDg8Po729HWFhYYiLi2MtoxfTXf58gau5xpW5ITNGRFkgNjYWFovFp8h0obBQkZiv9hGhoaFQKBSYmpri2UeQa5VdXk8tZPJZBBDz3XE6nWhuboZWq8Xq1avZTiouyIY/mztOs9kMk8kEu90uKjzq7/sQg0ajQVNTEzIyMliNORLZEXDlXJYsWcK2L2u1WlaVmrSRk9bc000INBBwPxeArywwPj7OFumF8zOnAnOZdvMHUvYRXV1dMJlMOHbsmKR9BCAb650qyORziiHmu2MwGFjnzg0bNkiaonGLrYH8URBSCAoKQl5e3qyIRyzyoWka7e3tGBoaQklJCdvZ5AuE7cttbW2wWq1wOBxoa2tjC9AkMjodhEDnAlxlAbvdjpCQEERHR/PmZ7hdYgtJ0oulBsVVqAgLC8PSpUt9so+QyWhhIZPPKYRwdgcAent70dnZifz8fOTk5Hj8cnO9ePz5oxc2LwwMDMzujcC9JmOxWFBXVweGYXh1KgJ/aydBQUEIDw/H0qVL2QK0VqvlpVm49SKpIv2ZhqCgIN4wp81mY9NPpGVZrVbzWpbngyBmG4HPB8jfRaD2EbLL6/xCJp9TALHZHbvdjsbGRphMJqxbtw4xMTFe1wlkvsZsNqOurg4AWFIYGhqadSGdSz6zaVzwBLI+twBNcv5kM5mYmOA1L5DI6FRor803xH5noaGhoi3LpJbmdDp5m2xUVNScbJjkWhZD5ENA07Tody9Q+wgpl1cuGckur75DJp8FBkmzHT58GAUFBVCr1aw1QVxcnF8OoP66kI6MjKC5uRnp6ekoLCxkXz8XjQtkjfb2dvT392P58uU8x9TZwtMfMUVRvDtbl8sFo9HI017jWmrHxsaesrrIXMKXSEPYsky6xLRaLfr6+gDArRYSyIbJvTFYLKBp2qffs5R9hLDJg/s5kZsZ2eU1cMjks4Dg2lubTCY4HA4cP34c/f39oppp3uCrrI3L5UJbWxs0Go1o7cUfVWtPaG1tBcMwPs8H+Qtfr1GpVPKK9FyRy56eHjQ1NSEqKoqNik5HF1PA/1qfWJcYiRhJuzv3syN3/L6cg9y8LKbNNdAOSV/sI4iQLCEkUpeVych3yOSzABDO7pA/iNbWVigUioA3a/KF9hS1kBZnhUKBqqoq3owId53ZkM/ExASsVisiIiKwZs2aednIZ/NHKhS5JHURrVaL1tZWOBwOnsLAXKWiFgKzuU5hxEjTNIxGI3Q6HS/9REha6NHDxWJNu83F9YjZR5CbGU/2EYA7GfX392Nqagr5+flfeZdXmXzmGUJ7a4qioNFoYLFYkJiYiNLS0llt1p5SZsPDw2hubvZoo+1tDU9gGAZdXV3o6elBSEgIcnNz5zWCmKsBT25dRDiw2N/fD2AmFUU2XWHzwmLZIOZ64JV0gMXExLDpJ0+bLDd9uVjTbvPxfRR2Ygoja5PJJGofAYAdqSA3jV9ll1eZfOYJ3CE2cgdG0zRaWlowOjrKTmvP9o9DLPLhKgmsWrWKFbj0tIa/G5nNZkNDQwMsFgsqKipQX1/v1xqB6MHNB6RSUUKFAUJEwvmkU4n57i5TKpW8O36x9CVRoiZt+otps1yowWR/7CO4A60Enlxez2QykslnHiA2uzM9PY36+noEBQWhqqoKDQ0NcyqNQzA9PY26ujr2PGJpNiH8jXy0Wi3q6+sRGxuL1atXs4KNZ4KlAjcVlZOTwys+Dw0NwWg0QqlUor29HXFxcad0qJNc70JBbJPlWo0DwNGjR3lq3aeylnaqVDE82UdMTk6yRpDe7CO4ZHT11Vfj+uuvx9VXX73g72e+IJPPHIMrkUO+TAMDA2hvb0dOTg7y8vLYEHuuyIesMzQ0hJaWFmRnZyM/P9/nPzxfIx+GYdDT04Ouri4sXboUWVlZ7OY3l1I/YjhVd3zC4nNnZyeMRiMoimLvaoVzNAs51Hkq74RDQkJYW4Tp6WkcOXIEqampvLZurnXEQg8CLxZJJq59BLlJi46Ohl6v99k+QqPRzIsh4anEmfVuTiGkJHKampqg1+uxZs0aNn0BzGz4JDKaDSiKgsPhQENDAyYmJlBaWsremfqzhjfyIXNI09PTWL9+PaKjo93W8Pec/mIxCIsqlUp2ah6Yuaslw64tLS28DXe+mxcWw+dBwDAMa6MtbOvmDgKT7rC4uLh5VzFfLOTDhcvlgkqlYi02AM/2EU6nE5mZmTCbzW6D2t7w5Zdf4oknnsDRo0cxMjKCt99+G5dddpnH1+zZswd33nknWyu+7777cMMNN/CO+dOf/oQnnngCGo0Gq1atwh/+8AesX7/er2sDZPKZE4il2fR6Perr6xEVFYUNGzaw3S8ESqVyTiIFhmHQ2toKlUqFqqqqgIYpib+OFPR6Perq6qBWqyXnkM7UyMcbQkNDeV493Dka0rzgiz1CIDjVkQ8XwmsRq6URiRuSpuPO1/jT1u0ruNmHhUTjsBG1/UaszlKjJE3Ne06sCcKTfcSDDz6Izz77DAzD4O2330ZMTAzWrVvntp+IwWQyYdWqVfjud7+Lyy+/3OvxPT09uPjii3HLLbfgtddew+7du3HTTTchNTUVW7duBQD861//wp133onnnnsO5eXleOaZZ7B161a0t7d7rS0LIZPPLMGd3SFf9O7ubnR3d6OgoADZ2dmif1CzTbsxDIOhoSFYLBakpKRg5cqVAf+hSaXdSGvo8ePHvcr9zHfNZ7FYKniCcMMVs0cIDg7myQBJtS77gsVEPt5ERbl6a1lZWazEjVar5bV1c8lotqoUCxX5aIw29GstyIpT4Q97evBu4xj73KUlSXj00mXsz94IUWgf8cYbb6C+vh5bt25Fb28vLrvsMpjNZtx222349a9/7fG6LrzwQlx44YU+v4/nnnsOubm5+N3vfgcAKCoqwr59+/D000+z5PPUU0/h5ptvxne+8x32NR988AFefPFF3HPPPT6fC5DJJ2BwZ3eIRA7pALNaraKpKS5mQz5E8XpychIRERFITk6e1R+ZWNRCUoY6nQ5lZWXswKYU/O2YI6Q9m813sUNoj8BtXhgcHERrayvCw8N5czT+5vUXC/n4KyrKlbgRqgoIBzlJY4cvd/tcLAT5vFU3ggc/7ADNABQA4V/Au41juKosjY2AXC6XXzVBhUKB0tJSuFwu/PnPf0Z+fj6am5vZ4dW5xIEDB7B582beY1u3bsXtt98OYCb1fvToUfz85z/nXd/mzZtx4MABv88nk08AELO3npiYQENDAxITE7FmzRqvm0ig5GM0GlFXVweVSoUNGzagrq5u1ukuIXEIz+HLH70/kYlWq0VdXR3sdjvUajVb0Fer1R5nkRZ75OMN3OaFvLw8tnVZq9Wiq6sLFouFLTyTz8PTRrWYPo/Z2imIqQqQDrHe3l5MT0+z7cpkdsbb35i/5MONYFLU7jdFwuc1RhtLPIA78RDUDRgDJh9gZtN3OByIjIyEQqFgnVnnGhqNxk39JDk5GUajkU0Fulwu0WPa2tr8Pp9MPn5AzN6aYRi0t7djYGAAxcXFSE9P92ktf8mHYRi2ay43Nxd5eXk+KRz4AvI+GIbB4OAg2traeOfwZw1v74GodhcUFCA6Opq9221sbARN0+xwp5gy9WLabOcCwtZlq9XK1ouam5vZ5gWubYTw8zhdIx9vEA5ycmdnOjo6YLVaRTvEuNfjC/kQQmkeMeKZz3tBM4CCAq5bn4Fr1qezJMSNcBQU8KuLCpARo2KJxxNKM0/WfQIZfJ2engaARWUcOBeQycdHkKaCxsZG5OTkICIiAmazGfX19QBmFKL98cNRKBRwOBw+HctNgYl1zc2FIrXL5UJjYyMmJibczuHrGp6uw+l0orGxEQaDAevWrUNkZCQcDgciIiLYQivXc4UoUxMimovOwLnCfG34YWFhbs0LpJOut7cXFEXx6kWLiXzm20hOODtDiFqn0/E6xLiddHobcGxwCnnJMwQkjGpeOjCApz/rcYtYaAbYUTOIHTWDuHNTLi5cnsSLcGgGePDDDvx8ax4oCvD053dpSRKv6SCQJojp6Wm2FjSfSElJwejoKO+x0dFRqNVqnqq32DFERd0fyOTjA7izOxMTE0hPT2cVojMyMngK0b7C11ZrYixHutmENZK5iHwcDge0Wi3bzRZox5wU+UxNTaG2tpZ9DyEhIW5KAcKCNLcGMDAwgKmpKSiVSnR0dLAb8OkoBuoruM0LmZmZPA+asbExdHR0AJixP3e5XB511xYCC02EQqLmWkcMDg5i37AL/+xUgjnWBnJVDE5GLQaLA0991uv1PE991oMBrcUtwqEZ4NGPuyRfd9WaVFy6Ktmt2y2QtBtps57v+lVlZSU+/PBD3mOffvopKisrAczcAKxduxa7d+9mW7Zpmsbu3buxfft2v88nk48HiM3ukOFCg8Hgk3SNFLy1WnM7zfLy8pCbmzsvXXPDw8Po6elBaGgo1q1bF/AXXIp8yOBrTk4O8vPzfd6ghPWR/v5+aDQauFwuHD9+HDabzW2eZrHNdMwlhB40LpcLNTU1CAoKYnXXiJ4YKdAv5FDiQriYaow21A0aAADpMWGw2Gk2kgkPD4fRqYTZEYHo2Cy8sbeOjWi430qaAR74oEOyPiOGN+s0fl/rhvxYN+IBAiOf6enpgGaipqen0dnZyf7c09ODuro6xMXFISsrCz//+c8xNDSEV155BQBwyy234I9//CPuvvtufPe738Vnn32Gf//73/jggw/YNe68805cf/31KCsrw/r16/HMM8/AZDKx3W/+QCYfCYjN7kxNTcFms0GpVGLDhg2zagX1NBfjcDjQ1NQEg8HgtdMs0Pkarv5bZmYmpqamZt0xxyUfmqbR2toKjUYT0OCrEEqlEiEhIVi2bKZtlTiZarVa1omVm5Ka65kRgsVSdyIT8GlpaYiPj4fD4WDv/Lk1Ea5txHySw3yn3d6qGxElDRLJAOClxjxhIX6DA1r3bjRSh/KXfIhQqb84cuQIzjvvPPbnO++8EwBw/fXXY8eOHRgZGWFn0QAgNzcXH3zwAe644w78/ve/R0ZGBp5//nm2zRoAvvWtb2F8fBz3338/+7f98ccfuzUh+AKZfEQgZm9NopDg4GDk5eXNegZBKvIhw6mRkZFsisoTAqn5mM1m1NbWsjYLOp0ORqPRrzWE4JKP0ELbF305X9bnQqVSIT09Henp6TwxUJKSCg0N5TmZ+tume7qAfC7BwcFuNRFSLxI6mMbFxSEyMnJOyWIuIh+xbrJ+rQWqEAUe/FA8WiH1F4ZZGFLxFdwmAwLy975Qkc/GjRs97g07duwQfU1tba3Hdbdv3x5Qmk0ImXw4ELO3JlGI0WjE2rVr0dnZOeeabOTcfX196Ojo8DrQ6Wkdb9BoNGhqauK5mRoMhjnrmBsfH0dDQwNSUlJQVFTksXXaX0j9IYmJgZIW5r6+PjQ3NyMyMpJN452u5nFCeKqzhIWF8aRuTCYTGxn19vay9gmEnGcbKXIjH08ty1LPCbvJLlmRhPebxnyKZHw5Zi4hNs/DhbDJgICbRfEHZrM5oMhnsUMmnxMQm93R6XRoaGhgC/EhISFzpsnGJQ2imzY1NYV169YhJiYmoHU8gVhcDw0NYcWKFbzulLmaoZmcnERPT49fLee+wp+NUWgFYLfb2SiAax5HyGiuo4CFgq+/M4qiEBkZicjISF7zAlddgESKJDLyN1IkRCgkEW7LsnAg845NufhOZSY0RhsvpUYz4KkELDZIfeoUgGf/rxgbCxJEnw+UfEjkc6bhK08+YrM7AFiTNKF681xpshHS0Ol0qK+v5xGcP/Cmywa4p8GELZuz1WWz2+2sVHxFRQWioqICXssTAiXIkJAQUfM4rVbLRgHcFN1cpAkXAoF2mImpCwhN4yIiItjPIyYmBhNmF5sC4xb6gRONAMNmME4XHvyS35K8o2YQL9cM4o5NuXjm8x7eQCbpJFuaEjHrlFlZlhpH+meXOvYXFACKAm/2R4p4gJPNBv7+zkwm0xk34wN8xclHaG9NURRsNhvq6+tht9tRXl4OtZofPs+VFQJFUbBarThy5IhHDThv8Fbz4abBli1bJppums2sEBEdpSgKaWlpPhPPqTKTE9NfI1HAyMgI2tvbERYWxpO8OZV+Pd4wF5/LuMmJ/iklspIykZ+fzzYvaLVadHR04PM+G97oUvAIwp9CPwOIztMAgXWSieFovxEXL0/Eh83jfhEZBWD7xmxEhwXh0Y+7eK/1ll5jAHy3EIgIopGXpEZerB1Go1FSyTxQZ1ViRnem4StLPtzZHaIUMDY2hsbGRiQlJWHt2rWirapKpXLWaTe73Y6uri44HA5UVFR41IDzBikypGkanZ2d6Ovrw/Lly5GWlia5RiBpN67iQn5+PiwWy7wTynx0mgmjACLrotVqWbdO4tdDBjsXC2YzW0NqLwd7dXh+/wBvBuby0lTQYdEwhoUgMjsN//q8TnQQ05+W5fn+1BgAHzSPgwKwPCUSzZppn1/3hz19UFDA10qS8F7TGG9o9NIS6doTBWBVSTHWpYWx9bS+vj4A4DV3EKWOQFW2A+12W+z4ypGP2OwOsbceHh5GcXGxx416tpEPcQENDw9HcHDwrIhH6nqsVivq6+vhcDhQWVnp9a7J3/dEhE21Wi3Wrl2LuLg4tLW1nRGWCkJZF+LXQyRvHA4HQkJC0N/fvyCeNJ7giQg9Ff25tRcuSOeYweJgpWY8nj/QC59HMIAk8XiKZGgGeF9APAxmHnv1hlJYHTT+eWQIn7ZN8p6/7c0WVrk6MzOT7bwUKnUQ0dhAvivT09Pzlso+lfhKkY/Y7I7JZEJ9fT3bduxNwiLQyIdhGNZqYenSpYiOjsbRo0cDeh9cCOs1k5OTqK+vR0JCgmT0JraGr3f0xKY7ODiYp7hwploqCP162tvbWRmg7u5udmMhzQsLqTIgFfmI6ZBVLYnjtS1LEQvNwKfJ/4WEP5EMF1xlAwJPkYzUY1YHjcxYFXa3T7ofAL5yNbfzMjs7GzRNs0odY2NjsFgsqK6u5llHePvOmEwm1njuTMJXhnzEZneGh4fR0tKCzMxMLF261KeQ2B9NNgJitWCxWFirhenp6TltXGAYhm2SKCoqQnp6ul+ioL5cC2nTzszMREFBAe/zmguNucUOiqIQEhKCyMhILFu2jLexDA0N8SwS5kplgDvrIiz062zAscFpFKaH8Ir/ws6xBz6YkeLx5bfjrc5xKhAI8QDu74MbyQzrbfjp262858XeO0UBmbEq9ItI7HDBVa7mgmuYp1KpMDIyguzsbF5zR3h4OE+ZQlhjDMTF9HTAGU8+DMPAarXCYrEgLCyMbZUmfjj+Tt/7G/lMTk6ioaEBsbGxWL16NbsZzVXjAnk/R44cgcViEW2S8GUNT8RB0zSOHz+OwcFBlJSUiE4zn6mRjxDca+BuLEuWLOFZJBCVAa5lhL8SQGLpMW6h/4FDDJhDHaAA3LQhExU5seieNIluuj6/Pz+OnSuQTV8sUhEeR7rLhI/Di8AnAYlkVmWofSNaBqgbNCA9JgwKkXMTiA2VCuFyuRAUFMQbAyDfGRJJm0wmVq2boijEx8fPqtvNH8vrjRs34osvvnB7/KKLLmIldm644Qa8/PLLvOe3bt2Kjz/+2O9rO6PJh6TZhoaGMDw8jPXr18NoNPKEOv1VKvCVNLiRyLJly5CRkcGLRMiGP1tBRovFAr1ej+TkZB65+QNPGzupHzmdTlRWVkoWPheCHBYD+XiC0CKBiF12DE1gd9MAEkIZLEmJhSskClNQISYqHFaHe9uyp/QYP5KhTvw/8Pf9A/j7/oEFe69ziY1Zwfi83+GVCBgA39+Qhef29bs9fovI44B7NMONZHwhaQbAXW+3eRx8lRoqFUKs4UD4nbHZbGzzwt/+9jfs2LEDoaEz2nUlJSWoqKjwObXrr+X1W2+9Bbvdzv48OTmJVatW4corr+Qdt23bNrz00kvsz4Gmms9Y8uHaWwcFBcHlcrFeMkuWLMGSJUsCbm32FvlYrVbW0VRq7oV8CQNtvyTeOEQUdNWqVQGTmBShcutHy5cv93id/pIPkcT31b1zsQ+BihX4VSoVPmrX48FP9TODlRSFTbkOfNY94NbSe9u5WYiLDPVJn2xxU7B06k40rQXg836H22OQWGN5WqQ7oZx4XBiZKAC4fas9RDKKE9GTlIwPt/nAZHdiQGtFaabaJ+IBfBMVDQ0NZWfSnn76adxyyy247LLLoNVqcdVVV0Gv1+Paa6/F3//+d6/n89fymhj5EbzxxhsIDw93Ix9yjbPFGUc+wtkdsrGaTCb09fX5ZAntCd6GTImjaUJCgkdH09mQD/EVMhqNyM/Px8jIyKw2Z66ZHPnvnp4edHV1iUZtntbwBRMTE2yTB9eHJT4+XnJGAli8kY/UVD/Ab0dmGGB3t8nt9QyA33/Rh5Pb7umN758lHoX8Yls+Hvm4k/eYVLTx9SVB+F+30+05m8P9FQyA2/7dgq9xmgkUFHBJfjje7TC7HcuNZLit1QwD3hpC0AxQO2DElqJEUadTbwjkb33p0qVQqVS49957sW3bNrS1tbn56YhhLiyvX3jhBVx11VVu2Y49e/YgKSkJsbGx2LRpEx555BG//b+AM4x8yOwOIQeKoqDValmL1w0bNsx6YFCq5sOdq/Gl4M8lH39gMBhQV1fHCo8aDAYMDw/79yYEINdJiJsQG2mO8HUNX5xMuaSWmJjIa2Um6tRkwJOoU3OvcaEhLPgzZheig6XTY9yp/itWp/gRpZx+xCMV4bhoWjQ6YSQ+DbFjN5ctxXs9LTwSoMCgtlV8tkjYTDA8MoLkCCXe7zRLEomn1uphvQ13vd3qdq4ndnXjd7u72Xkof0BqPv6CtFpTFIWioiIUFRV5fc3ExMSsLK8PHTqEpqYmvPDCC7zHt23bhssvvxy5ubno6urCvffeiwsvvBAHDhzwm1jPCPLhSuSQbjaGYdDR0YG+vj5kZWVhaGhoTibVvc3V+CovQ8jH1+YFrr8PV3h0LhoXyLUYjUY0NDQgPDzcb6kff5xM169fj6ioKNjtdjd1aqPRCK1WC41Gg+PHj0OlUiEuLg5BQUHzOkdEwE2fVXdr3dJgFIBzs8PwZX+N16n+/9TOzfT+QkIqNSb2Vp/4xjLU9OrxpuB9vnBgULSe8ujHXW5riRXxxSKZmccpvN7mlLwemgE+aR3HKzVDrH6ct0hG7DGrg8bW4kSY7E6P81BVS+L8ioBcLldA6uqnQl7nhRdeQElJiVtzwlVXXcX+d0lJCVauXIm8vDzs2bMH559/vl/nOO3JR2x2h1skr6ioAAD2rnq2EEY+RL4mKSkJRUVFft3Z+KoTx7XRFqYN54J8SFRx+PDhgOthnshnenoatbW1CAsLY0lN7JopinJTGyAyLyMjI7DZbDh69CjbPaZWqwOKiKTal4XdZWKbHANgT5+7V8uZAqnUmFh0khYThm3FSW7k461mRQhHQQFXlKa4vZ6c8/2mMfz+ymLc9u8WnjEcBXHSosBgx8EhtzU8RTJi1xYWrMChXj2qlsRh5/ZyfNI6jid2dbu9xwGdxW/y8Tc6IFqE/iocJCQkBGx5bTKZ8MYbb+Chhx7yep4lS5YgISEBnZ2dXy3y4UrkEJdRMouSmprKapmZzeY5UaIGTm72NE2jo6MD/f39Aas4+0IcQgtqYWfJbEVBXS4XG4aXlJQEXEiUug6NRoPGxkZkZ2ejoKDAL7IICgpiO4ESExPR2tqKlJQUNwO5uLg4jNhC0DJmQ1Z8GMKDg0Q7yKSiGQUF3H5erpv+2OKsMPkHf+d2DFbxGTYxEr7mpTrcsSnHYwuy2DoXFSfig+Zx0MxMdOgpkmkenhI99xOXLUPTyBRePjjESgOty1Sjpn/KbY3BkTFsLE7HAxcXeGzoIHWga3fU8QZ0txQl4ne7u92+M5mx/gnQBlLzsVqtcLlcfisczMby+s0334TNZsO1117r9TyDg4OYnJwMaAj2tCQfKYmctrY2jIyMuFkGKJVKNjU3W8MrhUIBp9OJQ4cOse3HgYbE3shncHAQra2tyM3NRV5enqSNdqCFeLPZzIqCAphVI4bw2rizQStXrgzI6VC4vkKhcDOQm5ycxMOf9GL/sBPcuglFAQ+ICF+KbXQ0Iy18ebqjKkeNFenR+KuPbdh/2NMn2p4s9hVjADzzeS9urMp0a/P2NJPzQfM4bw3JSIYCntvnft0K6gT5rcvANesyMKCzICxYgWteqhM9dlqvxSs7B5AZHYo/b4tHnU6B5w6Oux1779Z8PLazk1e/e/DDDrx6Qyl+dVGBm2qEv00HgUQ+JtNMg0oge4w3y+vrrrsO6enp+PWvf8173QsvvIDLLrvMrYlgenoaDz74IK644gqkpKSgq6sLd999N/Lz83lup77itCMfKYmcuro6BAUFiUrkkF94oMJ+XOj1ejidTkRGRqKoqGhWpmRS5ON0OtHS0oKJiQmsXr2a1RnzZw1vICKqqampKCwsxKeffjqrCIob+XCVwT3NBnkDNz02pp2G1XLy+ppGplDbb0SUKgz7h10QFuwZRlz4UopgzkTiAYD9vUbs7zX6HQFxj2cY6QiKZgClSDDLYGYmZ9Jkx39qNWx0IhZ1SEUyYoRHnbge0rFGCv+HevWi11eRG4NHavSgGSUUlBO3rHViSZgFFBh2TgonzhetChKt71zzUh1uqsrEzRsykRgZinML4gPqdgtk/zGZTFAoFAHZfHizvO7v73e7nvb2duzbtw+ffPKJ23pKpRINDQ14+eWXodfrkZaWhi1btuDhhx8OaNbntCIf7uwO+dAGBwfR1taG7Oxs5Ofni/5yucX9QJsOyJ08SfcsX7581h1YYsQh1E7zNgTrL/lwGzG4atezHRIlrycWCzExMR5bzcWgMdpQN2gAAIwYbDz/F2Bm47HFjeBov8Ens7EzlVBOgsQNMwiEYMSUAaTW8Cc6AYDn9vVDQQF3bMrBijQ1Jk123PW2e6cVJRLJSB3LPT2JTAqSIpAVp3K7PgrAge6TpEQzwHNHDXj1hlLcF2HEo5/MpNIUAL61hEaQrl+yzvf36pPvsWHIiEcvXSb+IXlAoJHPbMRrPVle79mzx+2xwsJCyX1ApVJh586dAV2HGE4L8uHO7hB7a6KsrNPpfIoOfDFdk4LZbEZ9fT1omkZZWRlqampmrUxArotLHMPDw2hubkZWVpabdpoUhDM6nmC321FfXy86/Drb2hHxJzp8+LDf/kQaow2vHRrCyzXuXVJcMPBPxv/MB//z3bwsHrvaJiVbkcUeOzfZhS803jdEqUjG2/0Kzcyk5l69oRSlGdHi3W2cSIbMSGXGupOJ2GtJZPLAxQX81BiAK0pi8WajTvL4ndvLUT9oBM0wWJYQghCnCTeXavD3OneJIi64QqL+IBDyIS6mi33IOhDMLge1ACBNBdyhUYPBgOrqajidTlRVVXkkHoJAW3VHR0dRXV2N6Oho3oY9l1baRGuutbUVq1atQmFhoc/hOTnOW9Si0+lQXV2N4OBgVFZWuhUwZ1M7crlcGBgYgM1mw9q1a9k2cF/wVt0ItvyhBju8EA/BmU48Yp8aJfG4ELvbJ3HThkz4s08R4iEvoTx8ws/t68d/6zS4qSoTd21egp9vzfPp90E2/OpuLX51UQEUFDmX+3E7agax5Q81bscqKODGqkz2Zy4YnGx9fvWG0plrWx+Cb5bEezz+o+ZR3P1OK+5+pw2XvdCAmnEFbr14LV69odTr51034L9raiANB2eqlw+wiCMfKXtrMqTInXXxBSRa8hWkgWF4eJjXwEAIbK5EQS0WC2pqakBRFKqqqvzO7XKHVcUIizsf5CkiCTTtRpoWXC4Xq+jsK0aNNjz4oRzJcOFr1CIGmgFrDBfoea8rS8ErR0Y9+t6QFBQhRe6xUhI1ZMPfub0cO7eXe02tkWNvPy8HT3824y30QvWApL4azQCvHR7kzfj8VGXmRUPC45/+rJeXkiMEtjJd7aUzjoFS14f2dpNfbreB1nzkyGcBQYYNR0ZGWOKx2+04cuQIBgYGsH79euTm5vr1C/F1pgaY2VAPHjwIvV6PqqoqXufcbFN4XDgcDnR0dCA2Nhbl5eUBFRU9KSU4nU7U19eju7sbZWVlHsk6kMaFiYkJHDhwADExMVi6dKnvaTaDFTU9Ovxtf7/PLboyfAOvSw3AteukjRHF8I+jo7hjU65oxCB1Lu6hRKJG7PVkNoYcR/TVxEAzQP2gEc98zicIMvsjfJmCAl4+OMQZSAV+9+UwGw2JHS/W9Uiuj1yjGL62IglbygpBURR6enqwd+9eHD58GJ2dnZicnBTdG8jNtBz5nMSii3xItEMkxjds2MDqpcXHxwes3OyrFQKZE0pPT5dMf812sJM0L5hMJqSlpfkklyEFKfIhg52hoaGi80FC+BP5cI3xyIzTxMSET69/8+gQ7n+vVSadWeKkXA3F+ZkPBsCrh4f9akSgGUBrtvM2Xk+vFzun2HAoMLPhNw0bcdNrDSf11yQimRlyYEQjloiQIDxwcQEe+LCDvU4ptYIBnQXrsmPwtZIkXpPK+YXx2N0+KTq7oxGJyCkA3z8rE+cUxLO1Hq7bLVGibmtr4+kVEisN8vcZaM3nTMSiIR/h7E5wcDCcTifa29vR39/vt0GaEN7IhwxbjoyMSHrWEPiibC0Fi8WC+vp6uFwuxMfHz1o2g3weXPIZGRlBU1OTxw5AsXV8IVQiajo1NcXzDvKFvDQGq0w8cwQGwHeW0khfUoiJaRuWp0Xhx2+2+PzZSs3hkAhCuIxUm7TU3JSSds6kvD7iE4Qw1UUUCD5pHee1Wd9+Xq5ogwIhiMxYlVdG5ZLJ+0387sjd7ZO4/bxctqOSnDNFHYpDvXpRyZ/1ObGiTQZcJWqGYVgrDTIMzTAMq5FotVr9stM+FdI6C4VFQT5isztOpxNWqxUTExOzGuQk8EQ+ZE7IHyvtQCIfIsWTnJyMoqIiNDc3z1ntiIT17e3tGBoawqpVq0Q9O7yt4QlEbSE8PByVlZU8nSpP5KMxWHGsX4+O8emvHPGQLSbQt+1pWFNro/DyiaFIT1GEVB2JzNZwJWk8zeHERYTgn0eG8GnbSTvpzctEIggA4z2tCA0O9trGTbTUfnJ+HuLCg9n6zjOf9yBaFSQ53Ck110PIigKDH56VKUkmNAOsSIvi1ZTIOauWxImS7T+PDGFddozIWU+CoiiEh4cjPDycHYaenp7G6OgotFotjh49yrNej42N9ThOEYi0zumCU17zoWkaNpsNTqeTnWInkiwAUFFRMSfML0U+w8PDqK6uRnx8PMrLy32yq/U38iFptrq6OhQVFWHFihVQKpVz6mZqsVhw6NAhaLVaVFVV+UU8gPfIZWRkBAcPHkRqairWrl3rJpAo9fo3jw5h41P7cMd/mvDnL3r9uqYzAQzEhTrFah1i98IMZibvxR5/t4/iTeOTdJfYumI1j1UZ0bhmXYbXzi5ybGasCrvbJ3nP7W6fxPmF8eC+y0tKkvD1C85BWGKWl5X50YmwvvPghx0wWBw8ywMCMtcjXOvGyowT0RiFP+8bxFt1I5LHhgUrRM85Pm3DjZWZbtf6adskGof963KjKApRUVFISUmBUqnEOeecg+XLl0OlUmFoaAgHDhzAwYMH0d7ejrGxMTgcfHmj6enpMzbyOWXkQ2Z3bDYbTyKnqakJLS0t7LDTbBUJCISE4XK50NTUxLY3L1u2zOdz+RP5WK1WHDlyBKOjo6isrGSHOsk1zZVSM7FZqKioCMjvXepaaJpGa2srmpubsWrVKkl9NjHyIWm2r0qw42tCmAHw043uG/PJCg5/TSkrAkZwNM3M+N2IXcfmZXyplEtWJCFFHSrq6CkE91ixCGJX2yTvyt9vGkPLqAkrcpK9Ni5szIlAOGzom3S3PhCm6UgXXOOwESnqULdW7NvPy+UpahMyAeB27K8uKoDFTkvODfVrLRBDIC3WwMkZH2K9vmTJEpSVleHss89mpbO4zQsHDhzAu+++C71ePysL7ZycHISFhaG8vByHDh2SPHbHjh2gKIr3TxiRMQyD+++/H6mpqVCpVNi8eTM6OjoCujbgFKXdxNJsZLI/JCQEVVVVUCqVaGlpCdjpUwjiZgqcVBEgcjyBtDf7EvlwnUDFpv1nSz6k8O90OpGbm4vCwsKA1xIjD5vNhrq6OjgcDq8yOcLXawxWfNQ8uijTbP4U4P059oaKdLzESWF5WqOntweA+/darIAvZkUgbDggj+ksdtE1drXxI5b3m8Zwdn6cqKOnEJ6O9WvwU6QN+/MeE97+shYxoZRPdgvctS8vTUXVkjgM6CysNbbY8fWDRrdjU9Sh0BhtkpYOn7RNiH4WpZn+DZYSSA2YcsVzgZPNCzt37sRDDz2EyclJZGVlIS4uDps3b8batWt92g/9tdAGALVajfb2dvZn4U3mb3/7Wzz77LN4+eWXkZubi1/+8pfYunUrWlpavCqxiIFiTpE9pN1uZzfegYEBtLe3IycnB3l5eezm/umnn2LTpk0BeWAI0dLSAoVCgaioKLS0tPilIiDEoUOHWIFLMXC7wTw5gR4/fhx2ux0rVqzw+xocDgcaGhowPT0NmqaxatUqv2ZshDh48CCysrLYyEyv16O2thZxcXFYvny51w5Do9GIw4cPY3nZBvz5i2786+jsDO5OV/iygUod64nouLUfBQX8oCoNf9ov/hm7retBiUBYK/J0vWLH3liViReqB0Rfo6CAndvLAcDjXA8F4GebMjBtMuHPNTrQJx77RqEK7xx3JxTu2lyNNY3Rhq1/dPdZogCWrIR250IbDS6qlsSgulvP/nxpSVJAsjrAzFhCd3e3mz+OJ9A0ja9//euIjY2FQqHA559/jvj4eBw/ftxrw0J5eTnWrVuHP/7xj+xamZmZuPXWW0UttHfs2IHbb78der1edD2GYZCWloaf/OQn+OlPfwpgxtgyOTkZO3bs4Pn8+IpT1nBALJSbmpqg1+uxZs0anooqIQWn0zkn5ENRFMbHxzE0NITS0lL2TiMQeGpesNvtaGhogNls5nWDSa0TSOQjdDM9ePDgnBjKEZkecjPgj0wORVHYN0zjR0/t+8qk2aTA3fy9RX7cYxlIExCDGXmbhMhgRKuCYbV49hTirct4FgYltaJ+rRVZcWGSXXPk2BsrM/B89SA7+Hnx8gS83zQumgYkkQZ3rkcs0vjt54PYub0cIRGjbKrt7XYLKlMVODDiklwbAI9MxIZKSbrOYHHgmc97ec0Ll5emoiApAte8VOd20/DgxYUYn7ahbsCI0ky133I6XAQyYKpQKKBUKnHBBRfghz/8IVwuF/r7+32S0QrEQnt6ehrZ2dmgaRpr1qzBY489huXLlwOYGe7XaDTYvHkze3x0dDTKy8tx4MCB04t8tFotamtrERUVhQ0bNogWsLmpstlgamoKw8PDoCgKGzZsCChE5EIqXabT6VBfX4/o6GhUVlZ6nXoOJO1GbBa4pm9zZShH3EYnJiawdu1avyKpFs00Xu/0ftyZAurE//gqyikGqWOloo/n9vXzzz9H69IM2JkcT11z5Njnq/l1lQ+aJ3BToQvPtwe5beAfNY3hv/Uarx15YkOlDICDGhpPfWMp7ny7w23tvc39eLlO70YmStqJ+z7qcVtfStGgJI2vaMDtqktRh86KdAgC0XUD+K3WSqUSubm5Xl8TiIV2YWEhXnzxRaxcuRIGgwFPPvkkqqqq0NzcjIyMDGg0GnYN4ZrkOX9xyhoOjEYjcnJysGbNGsnIxtfBUCkwDIPBwUEcPHgQarXaa1ujrxDWfBiGQU9PD44cOYKcnByUlpb6JLfhD2m4XC40Njbi+PHjWLNmDc/fZ7aioNz3YDabUVVV5RfxvHl0CNe92gzfS+6LF/40Ddx6bo7Px/uz7r1b83FDRboPBMP41TX328uW4clvFEk+D/Bnb8SOlZrrCVVSfN22E0T3Zp1GtCNPrPtOaqg0OkKFBy7mNwz83/Jo7KjV89Z+8MMO9I0bsSIl3G9Fg8tLU7FzezlevHYlXr2hFBkxKuzpmMArBwf97nATQ6Dks1Ct1pWVlbjuuutQWlqKc889F2+99RYSExPx17/+dd7OecrIJzc316s222zIx+l0oqGhAcePH8fq1auRnJw8Z51l3HSZw+FAbW0t+vr6sG7dOr/15ny5JiL3YzKZUFVV5WbyNNvIZ3x8HDqdDmFhYVi/fr3PBK0xWPFhkwa/fK814HMvNjAAlqdE+kQWf9jTi8rcWJ+EPBkAVbkxPq376MedyI0Pxye3luOuzUs8HEnhO4XA+Wn8pJRY5EM231UZat5GLgYye7O1ONHtWKm1QxQMrlg9s4E/+Y0iyfCLq1Ag7FQj/y1cOzNWxSOH28/Lwb+aDKJksnP/UYz2tuPqfJq3/hWlKZJrE6SoQzGgs+DaHXW48bUG3PrvFjyxuxvffqkOv3hXPGLwFYE0TjEMA5PJ5LeL6WwstAmCg4OxevVqdHbOpDPI6/xdk6TyyT8uTvmcjycEBQX5JQZKYDQaUV1dDZvNxqpezzaK4oJEPkRdm2EYVFVVISYmxu91vJEGUdWOi4uTJIZAFakZhkFXVxfq6uqgVquRnJzsc176+X29M/M7bzZ5ldU/3dCsmfZZYbu6R+fz+z/Yq8f2jdk+rfvghx2oGzRgdaZakigoAJsqSvHwN9fgyW3Sihyk4eCut9uw9Y81AIDHL5MunCsoYNJkh8Zow+WlqV5VnmkGeLpJibfqRpCiDkVseLDH1J8YmTzzeQ/uerttpj7FIY3r1mewr01RhyIzVsVLzQnXvuicdUhNTUVVCoVfVwVjU9pMO/WbtRq29kWOvf28XPRrLdAYbQDAyuqIpRvfbRybVQQUqJFlIAoHXAttAmKhXVlZ6dMaJNNC7LFzc3ORkpLCW9NoNKKmpsbjmsL2bS4WhcKBFPwlDG6xXGg9PdfkYzAYMDAwgLy8PL9FTrnrSJEPTdPo6OhAf38/VqxY4dEjPZDIh9stV15ejp6eHp8J7IV9vXji09OhwMNvRZ5PCLvRLixO5NlFAzPPidlUi4FmTnrceFIu+H8v1+FXFxUgIz4ZwKjbOlszXNg5ePKOm6Snfn9lsbg5HE4SFal9ZMSovF4vA4qtoYgZuwHiZAKA1Xoj74ligCtXJ+M/taPYUTOIVw4NsvUcsXZqsvavLipARlwkJhkbQkNDUVi8Gj+vruF9XhQY3LomAiaE8qR1yPv01CBSN2AMuP4zFzUff+CvhfZDDz2EiooK5OfnQ6/X44knnkBfXx9uuukmADMkcvvtt+ORRx5BQUEB22qdlpaGyy67TPI6HnvsMRw8eBBxcXGIjIyEWq1m/50y8vFls/aHMJxOJ5qamqDT6dw65/xdy9t5JiYmYDabUVZWNqv2ZinSENpQe/vy+VvzITI5ERERqKqqQnBwsM9raAxWPLHrdCAeAHCfHZkvMAC+WZqC/9TO1Dg+bB732jrtS5s1twZjddAw2Z08wU5PZKKggI2lS7FzsMttzVv/3YKLi+PwUav2hBwN8M3VKaxRnC9ri9VnPmkdx5aiRF7XGQWgMjcGB3r0PpEJA+A/taNu1yFFbBSAV28oRWLkjJROJGODUqmUWHtG/uaP+ybc1n/p2+KETBDojA8QmIsySbsFUvPx10Jbp9Ph5ptvhkajQWxsLNauXYvq6moUF59UzLj77rthMpnwve99D3q9HmeddRY+/vhjj2n6v//971CpVCgsLERvby/MZjNMJtOMxp3f72oBoVQqfUq7GQwG1NfXQ6VSSSo4z0YMlIBs2sBMXnU2xEOuSbjh63Q61NXVIS4uzmcban8iHyI6mpOTg/z8fPYmwJfUXcOgAW/VDp9WaTZfL1VsFkaKEMQepwDexk1iLrF1A+lGG9bbEBseDKuDFq113PbvFnythD+Dc/t5uSjLTYCC6hJd98OWSdyzRonQSDWWpcfDQIfizVqNz2sLbc4B4Ild3fjd7m786qIC1rcnLFiBa3fU+UwmUsRWP2jE1uJEUb23jjETrt1Rxz52/fIQfLtQfO2ExAQwmHBb/3BtI/7fslD8o83pdv5LS5Jm1fUWSM3HbDaDYRi/az4E/lhoP/3003j66ac9rkdRFB566CE89NBDPl+DzWbDM888g69//euwWCyseabL5Vrc5OOt1ZprlMZtPRZDoDM1BKTFOScnB0FBQdDpdAGvRcAlRIZh0NfXh46ODixduhRZWVl+NS54Iw5voqPeIp+fvdWMd+pHfLqe0xGXZrnwvz7+5kAIRBih3LMhBr/er3c7VggGwH1b8/DIx/zIQ4y8GMyIdwIUfvp2q9vxd73depLQJF4vnMERE+fkv4ZCUnoWIhgzjrT3g7ZbQCFIcu1XbyjFsN4GBgxKM6IRrQqSNGojZnDrsmMkhT3FoiRPxHbX260w2Z1uagUAeMOlNAPsaLLjgnU2UaKSUstev2Yl0lUuVOaM4/iIDlNWB6YRhrKcOFQUpPpkVS+FQNJuJpMJAE5rbbcXXniBHawVKsmctmk3h8PBDqj6MpMSaNrN5XKhpaUFY2NjWL16NRISEjAwMDBngqA0TbPzNQaDAevWrZvzxgUik0Nsx8W03zwRWMOg4bQnHrJhS0UzQuIhENuIJ83in7UbUVFAcWqU2+OipEbNiHeKrSP2WqmWZ+EMDiGBV28oFR2kHDABz3xOIpogbM6Pwq7OKfFOspZx/OPQEG8j37m9HO8c68Of9rtHTAM6C1LUoZI1ILEoiUjfiBEbg5MRE5nBASBpgUBkeIRrA3AjZJoBbniteSYduGY5NmAm8iDWCHV1dQDAOpfGxcVBpVL5TEaBupgqlUqvXlyLGRdeeCH730K35UXd7SZFGKTLzOVyYcOGDT6lvwIhn+npaRw4cABmsxkbNmxgzaPmIoXHvaYDBw6wxOAv8QCeoxadTofq6mqEhYV5FB2VEgY92KPFew2BDZHNF/y9+eRu1HORMfxbrdGnORIwQPOI+0Yueh0MUDdoQN2gewux2Gt/vMG9u83TLEtJmhpfK+FHu+cXxrMT/+TY3V1TePb/3OdwKDB4uWaIdywR7Tw3Vy36eYQFK3CoVw+AL+wpvD6yDtFnI112Yh153NkcAjHVauAkWQnXBiDaxUeuhRxDbBFKSkpw9tlno7S0FFFRURgbG0NNTQ0OHDiA1tZWjI6OuqlRCxFo5BMRETFn4sqnAtx9ibyPgYEBdHR0LP60m81mY3/mpqby8/P9mqlRKpWs540vv0xSGxHTgJttCo9gYmICTqeTNX0LNKQXi3y4KUlf0nhca3CNwYqXD/bjper+RSmV40/NSUrXbC4aEcjdPJkjEdZLGIiLgkpJzNz1dptkVCM8b0VWJKq6J1A9cvImyJs7p9BQbVfbpChZkTkcbrrq2nXpeOXQsNuxNc1dKE2LwHVFQWythHTocWswJLr5pHUcT+zqdlvntcODeKWGH1WJ+epw3483WR1Pa19emgqLXbx+RiI2LiiKYru0cnJy4HK5oNfrodVq0dfXh+bmZkRFRbFRUXR0NI9sAqn5nAl2Ctx9s6mpCc8++yybOTpllOpv2s1ut6O2tha9vb0oKyvzu72Z/OK9RSw0TaOlpYW1EBCz0p5t5EPO0d0980coZVPgK4QpM9Kj393djbKyMp/02cgabx4dwsan9+HFRUo8/kKKqC5b5R45SH1CYo8zAM7NDAZOTOW/Wavx2NTNHXi8sSpTcnaHETl+VTq/4HzJipkI5sAI/ztI3Dm5v2qGAaq7tZJdZWIRC6mjcH10EiJDRIc0Y4Od6Ovrm7FG4URF7zWOiUZJW4oSRdd5+aB4VCVmhVDdrcXWP9bgxtcasPWPNXirbkRyHklqbY3RJunzwx08lYJSqUR8fDwKCgqwfv16nHXWWcjMzITdbkdrayv27t3LDp9PTU3B6XQGHPmcCWAYBrfffjv279+PoqIilJWVnR5pN5I6AoCqqirExsYGtBbgmXyIkoDBYPBoyDabyMdisaCmpoatVQEIaECUC27kQ96DxWJBZWWlz58VRVE4Pm7FL99tPWXdbP5s/rPF2/X8mRjRtNmJxx+8pED08c/7Hbyrm9nM3VdhMBMZUZjZ/F6oHsAlK5I8EtBvL1vGSr00Dk/xnn+/aQzVfeJ1mbToMN4bIakns8MputHesSnXbXPHiddwU5XPfN6L289zP/acspWITc/Fv7rdmzWE10YiCiGhXLc+Q/J4Moz65DeK8Phly1CQFOFWqyFkQjTafF1b7FqIppu/CAkJQUpKCoqLi1FVVYV169YhISEBBoMBx44dg8ViQV9fH4aHh2GxiHsFCWE2mxEeHj6rG9PFgqmpKezduxcff/wxnnrqKTz66KOnNu3mzT2T+PwcOXLEL4VlqXN5ilhGR0fR2NiItLQ0r8ZygUY+ExMTqK+vZ220yRqz9SwiNZ/x8XHU19cjPT1dNGLzhE+7pvFMtT7ga5gLSH0T/OHCQNJpFIAfnZuNP+zpc3uuIjcGD3zAN8ySSrMBwA/OysBf9g25dchxj+XO7gzrbWwnG3f9tJgwWOw0hvRW0VTSs9Vjouk8Bu7Wc1Lt0oRohE6hUr44WrNd1FV0yODw+pkrANDGMeh0DGiG4a0TFxEkmV4DZiI37syQJzK5vDQVYZZJtE46sGVNHhIjQ/HKoUHJtYmqde2AEatnqVxNQFEUIiIiEBERgczMTNA0jb1790KlUmFkZATt7e0ICwtDXFwc4uLiEBMTIzoDdCak3QhomkZFRQX6+vqQmTnjErtoaz52u50N58vLywMqxAsh1nRALK4HBwexYsUKn7SP/I18iIxNT08PiouLWR8gQrxzQT4GgwEajQbLly/nuaX6Ao3Bit8fEDfP8g9iiZz5g1gb9IOXFOD+9zs8HicEA3HlAQrAgW6922M3laqRmCyeDomLVOH68gx2w1NQwKrkUNRqbLzjaAYwWR3YWpwIk93Jq69w6yXeakDcutPt5+WKthGT98gdVuW2KHMjHE9DpS8fHHI7tiApAqlRQaKfHVfx4ccbkhCpcGDv0UY8VMOAqNFxoyqh4gAxfONGOlLRKXk/b9WN4IHPtGAAvNIwo/4g1m5Nohuunw+3HjSXICntrKwshIeHw+l0svWirq4uWCwWREVFIS4uDrGxsYiOjoZCoTij0m4xMTF49NFH8de//hVmsxkxMTGLM+2m1Wqxf/9+KJVKhIWFzQnxAO4Ri9VqxaFDhzA5OYnKykqfRff8iXyIt8bw8DDKy8t5BnQkMplN/cjhcGBkZAQWiwUVFRV+EY/GYMWHjRr86+jgHKXaFjY9ILxkBnAjHrHjPIH7DhiJc/yt1ojHBLM7BI9+3IkdNTOf5w0V6Xj1hlLUCYiHnGf4eAN27T+CIKsBf7tyKV64pgSv3lDKq5eQaxAL+IXpvGc+70F1t9ZjZ5nVQWNddoxHW+zb/t3CSwt6Sl9d81IdjgyacONKFe/4r5Uk8aKbmOhoLF++HMl5JRDz5ukYGBGNqjzJ6ZD/FxIVOZw7zPrqDaW4a/MSvHpDKUsuQmITdrvNFUijE7nBDAoKQkJCApYuXYqKigpUVlYiPT0dFosFzc3NeOedd7Blyxa89957cLlcAaXl/bHQ/vvf/46zzz6bbSPfvHmz2/E33HCDm07btm3bfL4emqYxPDyM//73v7jqqqvw4x//eHGl3bgOoEuXLoVarWb76+cC3IhlfHwcDQ0NbArMn8iDrONt6MxgMKC2thZqtVrU30ehUMzKDoEoLhBfeH8mod88OjRT3wnozL5jLrrKTmLuIiux6/LnOrlXIvxv8v+v1AwhPSZMdN3rKzJgj1Lizl19YBgzKIzimqUKxKvDRY+/9dwc/GFPr1t0ISaH42muh9sppgpReI2SyFBpekyYW/qKHPvsgXE8c74aO7evFFU0IFFS1ZI4ZMeHi0ZV73VYeWs++GEHlscrkRkTJXo8Mb/jpsqkyFSq203qeLFut9mA3FxKpcHDwsKQmpqK1NRUVp/y7LPPxuuvvw6NRoO0tDRs3rwZF1xwAb71rW95nfvx10J7z549uPrqq1FVVYWwsDA8/vjj2LJlC5qbm3k3y9u2bcNLL73E/uzL/BHZIxsbG/GTn/wEV1xxBTZt2gSbzbZ40m42mw0NDQ2wWCxYv349oqOj2S6RuQKR6+no6EBvby8vBeYPyJdIKl3GFTj11hIeqB3C8PAwmpubkZubi+DgYIyPj3t/0QloDFbc/978Ew8gvaH7RkpCspkj4qGAZ68sxq3/bvHpmqRkbxgA923Lh81JIySIwqMfu2uoibVaUwC2FCXMbNBshEPhtQ4GV68Q36AyYkLd2p+35YTgwx672zkHdBasy44RNUjj1k88iZYSBQLupu3p2DEzjfNODH5KKRpIyeNctz4DO2oG3Y7/+HAbSuMZfLckHC82WnjXQdxWuWQiJdXDTRdyoyGp433pdvMHhHx8ucGlKApZWVn45S9/CYvFArvdjquvvhq7du3Cyy+/jG9/+9te13jqqadw8803syKizz33HD744AO8+OKLohbar732Gu/n559/Hv/973+xe/duXHfddezjoaGhPmeHCAj59PT0QKlU4h//+Af73KIgn8nJSTQ0NCA2NharV69m9cyIvM5sZC24oCgKHR0dYBgGFRUVAWsmkS+RGPm4XC40Nzf77AbqL/kQmZzh4WHWDnxwcNBnUdBerRlak110M11I+Hb6AJtLTvwPw0gQB3PyOEbwsNhmRCIAMdmbRz/u9Kg6wF2Hu9mKNRIwDPB645TbaykAYz1tCFFF4qkL0xASHolIxoKPmt1vOITFdG8yNMTcjStWStYRbtqejk2NOrmVSCkaeJLHEYuqXmgF7jk/G99YpcCK+HF0j08hPFiJx2vHRMlEOO/jidgIQXuqB80VXC4X2/DkD6anp5GQkICNGzdi48aNPr0mUAttLsxmMxwOh9vetWfPHiQlJSE2NhabNm3CI4884ibgLAR5z0uWLMEFF1yAlpYWVqz0lJNPZ2cnenp6UFhYiMzMTB7JeNrk/cXk5CSmpqagVquxbt06nwQ7pcCt1XBTaSaTCbW1tQgODmZDWF/W8pV8rFYr6uvr4XQ6UVlZyaoV+KLt9sK+Xjyxq5PnaXKqMLepOPc1GZz8QSpiEUY9BBW5Maju1rM/X7JiRlAyMdLmm+wN5T5bxGBGt61pZAovHxzCjppBj2QlTOd9rSQJTzWMgWZMoGDCVXk0ViQo8IaIv9nt5+Wy9Q8yhLkuOwYA8Ltd7gKjUkOlUpu22LE/XB+LhHAl75xiQ5/c9BvZ4L0d//hn/di0vRznZ2Vho8uFz1uGwNT2ul3XO8f68PXSTFxemgq1aQhOVSxK82fsG8S63bh+RYQITXYn+ietaBwO3DpBDIHuX2az2e9ut0AstIX42c9+xqb6CLZt24bLL78cubm56Orqwr333osLL7wQBw4c8PjeyFA/RVFob2/H9u3bcdtttyEqKurUkk9TUxMmJiZQXl4Otdr9l82dzQmUfLh1pMjISKSmps6KeADxWo1Go0FTUxMyMjKwdOlSn+9yfCUfonYdHx+P5cuX8z4Pb2s8L/DfOcVBj9+pOF/IipmDepCCmulu4+L9pjGcnR934hzermFGSPTRj7tEW6fvfqeNR5CeyOrJbyxDXEQIWz/hNiD8q1uBlHg1GLibm+VGK/Df2hE89BH/br5qSRxerhkSfc+ZsTME5S0akTrWPDGEj9r1+Ns7NbxzPn7ZMtz1Nn/DI1GHMP3n7fgUdSiUSiVWZCdDQfW6keif9mvw5/0juHFlOMri7MhMCEZyVAgoiuLbO5z4vLl+RZeXpuIPe3rwbuNJBYhLS5Lw6KXShnv+IFAjuYWy0ObiN7/5Dd544w3s2bOHd/N81VVXsf9dUlKClStXIi8vD3v27MH555/vdV2SraEoCj/60Y8QGxt7aslnyZIlWLp0qSQZkE3e6XQiJCTE7/XtdjsaGhpgMpmwfv169Pb2zpmVNul4C6RVW7iOp2vyRSZHag2NwYpj/frTxPhttnM+nonHF2ITi5JoxnfZG4oCzi1IQMPQFG8ju2RFEix2WrRYL0VWqzKiPdZPbFCKzvn093ThyTr+e3rwww48ftky0Wu/rnwmOjjUq+dFSW/VjfBIkRKkpLjCngd7HfjrsWneOR/4sAOv3VAqmsYMC1aIdpm9KnG8UE7Hk0r3i40WZJcxGG3pwq6GfixNjcGGjES8//3VaBm18maqyHnjIoJ5vy9gxrn0qrK0OYmAAr15DmTOZzYW2k8++SR+85vfYNeuXVi5cqXHY5csWYKEhAR0dnZ6JB9CupdffjkyMjLgcrlgNptPvZ9PRESExzZjiqICVqPW6XSor69HdHQ0a5g2l26mSqUSVqsVLS0tcDgcqKysDOguxRP5uFwuNDU1QavVoqysTFKtQKxj7vl9vXjy085THuXMF/xN3c2O2E5GKgoANKRrSePT7hpq7zfNbGRiG6sUWQEzhCDVkfbnQzqckxmCfYN2XvSQFh0Kpq6JdyzNAJ19I27rUADiwoPYOhA3SuK2LJP3VrUkzk1TDQBax23unYPMjAeRWE1FjIhJG7jY8WJRkieduL2jSuwaoEAzNKh6La4vNmJ1tBWjDvdOQpoB9nXqIIbZOJdyESj5BJJ241poE4dRYqEt5e0DAL/97W/x6KOPYufOnSgrK/N6nsHBQUxOTko6LJN025///Gfs3LkTN9xwAzZt2oTo6Gj2mFPeau0NgVhpE/FRoSrCXKlREzQ0NCAxMRFr164NOJUnRT5msxm1tbUICgqSNMjjrsGt+Zw+NtfeIUUyYsOkgHRn2sn1Tg44SsFTd9tNpZFwMgqkpSa6dbcxAL7s0EpurJesSBIlGSFZvdc4xlMikOoy2zdoZ4dGw4IVsNhpSbL66zEDKpKBmtGZ96+ggB9uSHdTtSZRkliUJtWy7K6pcPJVwuYCUo+SinDE0n/CJgnSTr6lKBG/293tts4n/TTnCoBXWp248ntlSDQYQB3pcYsW12WE41/H3K9+Ns6lXMzGQjuQG1p/LbQff/xx3H///Xj99deRk5MDjWZGjSMyMhKRkZGYnp7Ggw8+iCuuuAIpKSno6urC3Xffjfz8fGzdulX0GkjEU1xcjEOHDuEf//gHXn31VRQVFWHDhg0oKSk59Q0H3uCrmylw0uNHyhdnLiIfhmHQ29sLu92OrKwsFBUVzVoUVHhNY2NjaGho8Fkmh0tgDYOGRUc8/kQpYvMyYrA7GfFZHS8n8oV4fr4170QnGz8dRgH4e930zH/XG0XP/9y+ftF0WFiwQjQiOjs/TnSjZzib7ftNY/j5ifQcF4TUBnQWn9qnD40Bz39rGca0eoS7TOgcHQDNKNzWNFicfrUsF8a6byMUTvoTcVN0wIxcjq8pPam0o1S3mlSjxKiJxrq8TDxwcRDv+O+sCEPoZAcqkhU4yMlUzda5lHd+H5X0uSAW2oF05Pprof2Xv/wFdrsd3/zmN3nr/OpXv8IDDzwApVKJhoYGvPzyy9Dr9UhLS8OWLVvw8MMPe7wpZhiG7dQ7dOgQdu3ahb179+LgwYPIzc1d/OTjzc2UwGAwoK6uDhEREaiqqhKtESmVStjtdpFX+wYuuYWHhyM+Pn7WLeDcwVeGYdDZ2Yne3l6/ZHII+SzU4Ki/8Jl4RIrvUnjkY3GCnc17p3ByNkdBARcVJ+Cj1glesZ97HgrSUZIvrdVSG70QNAPEqoJ9rp94IisqOBSXrC8EACzTmfGnliNu537k405cuCwWO9t1Xjf1T1rHsSSIwfb1sfjTIR37uTxw8YxuHKklETIRqhCQD7NqifhIQlacStR4z1M7+cs1g27kL3V8ijoULpcLK1cacLBDg2P9OqSH2LAidQpdXV2sPcJsPHVmE/kEqu3mj4V2b2+vx7VUKhV27tzp9zVw98b169ezjqbV1dV4++23T/+0G3eg0xcr7UAjH6ImEB4ejqqqKhw7dmxO3UwdDgfbHOHvDJJCocCkhcb9Xy4+4vEn6vFEPP4Qky/n55LDFatSUJgSwdusaQb4sGUc1xcFYUer+HeGAfD9DVl4bl+/2+O+tlY/+nEnT/BTGPmRa12VEe2Wtjs7M1SyfiJFVr4W73e26fCTUsCmjEBEVCQK09R45ZA7ST6xqxsUgO3lcfjk1pOOocT2QJiik7J2IAZxwnqSKASvF0ZWl2bTeK9fITm7Izx+3OREv1GBNUV5uKg8FHa7HVqtFlqtFs3NzXA6naxPT1xcnN9K07Op+Zzu2m5jY2OsqgLDMGAYBlVVVaiqqlr8kY+ntJvT6URzczO0Wu28WmkPDQ2hpaUFubm5yMvL86qQ7Q8UCgXMZjOqq6sRGRkpKsPjCRqDFa1DRnQZGNDMqZjgIfe60s+KwdvdvvDYq8tS8dphdytvso7Yxk6UDMSGIl+9oRSftI7j5YNDeLNOIyG3Q0kSD1lneVqk6CavszjwSg1fiFMsUmLgLvgpbPuVqg3tHbDh+yI1HimyumRFku8tzgAGqUS8cXQcDEygoEFFqgI1GkaUPP50SItL1wPrsmMkNdM8qQo0DRtx02sNomTl/nuRlsD5b+0I3u2j2M/79vNyPAqFSgmLpqSkICUlhU1/abVaTE5OoqurC8HBwTwy8taJGwj50DQ9q8jnVIOkGn/wgx8gODgYN954I84//3w2gnQ6nYtTWJQLKcKYmprCgQMHYLPZUFVVNS9W2kStoK2tDaWlpTy30blyM7Varejv70dGRgbWrFnjF/G8eXQI5z29D7f8qxUvtc/6UgKE/4RHAbhtY67PxzIMJInnR+dm45azMkWtn3GiJnLHJneDtSN9ejdy8A8zm/Bt/27BBQXRrNAlidAe/dh9oJMB8L0NWW4rkdoNaXMWqw3VDRo8dogJhTbF1nmvcUyUFNJjwtjXEygo4I3acc7nQ6FGw+DRc2NwZZ7775zUYQBpjTUpD50ZRWv3xgdvhm8aow2HevWsEKjGaMNDH3VAqJitMdrcjiXHexMWpSgKkZGRyMrKQmlpKc4++2wUFRUhJCQE/f392LdvHw4fPozOzk5otVrRPSGQIVOTyQQAAauwnGoQkjn//PPR19eHW2+9Fddccw3++c9/YmRkBEFBQYs/7SZW8yGRSE5Ojl/20/6Qj9lsRl1dHSiKQlVVFVQqvt7TXLiZtrW1wWAwICUlBXl5eX69XmOwCuo78xP1+NvS7AtmNoUen84ndW4i1y/mwcN9LZnREa759Ge9fg20ukdYJze4T48bcHuJCzZlBP5UZxV59ck1zimIw9/297vd+ZvsThzq1UNrdpc+8tQEkBmrwoDO4pMnD8N5nru2WIuzVI0nOSMLN68Iw3//dIh/LWBgnRjAaJgNaeoI0WsVUxXIjFVJkpWUFpxU+3VGjEp0nbkUFlUqlWzEA4CXomtpaWFTdCQyIuMk/txUAifJ53RPu/3whz/ExRdfjI8++gj/+c9/8MADDyAvLw/f/OY3T4+0G9nkXS4XWltbMTo6yuqaBbqWJxDF69TUVEljudlEPlarFXV1dXC5XEhNTfVJHZaA6LN1j5nmob7jnkI7pyAeezsnfU6RzcUV+HScH9cjdih5p8JCtlSajqgo6ybG8PyJjjcCGoArNhtRjA2AOPmQDT0xMtStzkIzJ+V+fK0NKSjg+2tnurGErqNSnjwUTpI297rECMyTwZtQQ40C8P2yaAQHh2BnbTciGQuuK1LhlVbHScJm3FUFuBu8v1pwYu3XUkOq8yksShxMhSk6rVaL7u5uBAUFQaFQQK1Ww263+zwsbzabERwc7NfesFiRnZ2NW265BTfddBPeffdd/OMf/8AvfvELUMxsPZxnAYZhvHaftbe3w+l0IicnB3V1dVAqlSgtLfVJN02IyclJNDU14dxzz5W8Hl+7zZqamhASEoKlS5f6dQ1arRZ1dXVISEjA8uXL0dHRAZqmWbE9T3jz6BDuf69VssYxHxArgM/nuWZ7Hl9rSWLHUQA+ubXcreayKj0KjcNT7PFS1yn2WVEAqpJp7B9VsOe9/8ICLE2OcLM84L5GSBLktaQ2ND4yBKuLQXhsklu9hqwh5VwqjBiqlsTxNnNyLjGDN1I/eatuBA98cJL0LsiPwu6uKfbYH29IQn6EHcf69XihlX9To6CAndvLAZxsMOBGMsL3vHN7OY+oDvXqceNrDW7v+cVrV6Jr1IjHPu1hZ5nEIjhy7LrsmHk1k3O5XDAYDGhvbwdN07DZbIiMjGQjp+joaMl0XH19Pb72ta9Bq9We9jbaNE27qdR0dnaeHmk3vV6PAwcO+K2bJoSnaMVut6O+vp41ZfOWaw3EzZQMv3JFVH2dYyI2CGJtv3MH98hnIe9MJFNsPl4HiVCah6fw130DbiTAPYfUEOkXHZNutZL6IXelaTHyIp8et5OObOAE5M77OyvFfXvIOmJddNy5ngd2T544n1bSm0jYyJCiDuXJ5nizzV6RFoVXbyh1s5gWa5f+tHOK99rf7x/Dzu3lCI0344XWRre1/7CzEe93mL03PoikwaQilrBgBb62PB5h+h6kF670qFEnlQKcS0VrkqJTqVRISkpCQkKCW4ouJiaGJaOIiAh2T5yenj7tU27AyWYLQjxjY2NoamrC8ePHF3fDAU3TGB8fh16vR0lJiWQKzFdIpd30ej2qq6tZNQFfinz+1HycTicaGhrQ09ODsrIynj6bN203jcGKgz1a/PmLbi939HNBE77fYS3kvditG3O8XgOFkz4vz+0bmHmMU9S+aUOmT5/QIx93eo2cGAC/vWwZ7tq8RPK5J79RhMcvW4bU6FBRknqxwSz5GZLakFihncz1cNNsgLjTKbeRQczpk6ToiCqC8FxNw0Zcu6MOT+zqxrU76vBW3UzTh5S7qPDcAzoLax4nXPvd42a3tFlsMC3ZXMCFsGmBrHHtjjr8r3Ec8SoF+56Fx3KFRbf+sQZv1Y0gRR3KHj8fIMKiJEVXXFyMDRs2oKysDHFxcdDpdDhy5Aj279+PlpYWvPbaaxgYGEBkZGRAUY8/LqYA8Oabb2LZsmUICwtDSUkJPvzwQ97zDMPg/vvvR2pqKlQqFTZv3oyODnd1ETEQGbJPPvkEDz30EP7f//t/+MEPfoBHH3301JOP1IdrNptRU1MDq9WK6OhoN4nwQEDIh2QaSTRy+PBh5OTkoLS01GeZHF8jH5PJhIMHD8JqtaKqqspNn80T+ZButut3HMO/jg57OdPChua+Up1wMwkEz+7pdXuMAnBTVSbveoT202CA+7bl4fbzcvD8/gHRtQPJaJBW5i1FiaKb5bDBirvfacVdb7fh7hMND57W4v0M4MaV4YjHNO69INetK6y23yhKZr84ocogXJu7cUtFOESDbTYdaGLvi1sf4q593foMt+NpBmhoace3Cyi3zj1CnNxutctLU/HqDaW890wzMxYMBjv/4i4vTcXO7eV48htFAOMuujrXttlCiLVac7voVq1ahXPOOQfFxcVwuVx46qmn8P3vfx99fX245557sHv3blit0o0sXBAX01/96lc4duwYVq1aha1bt2JsbEz0+Orqalx99dW48cYbUVtbi8suuwyXXXYZmppO6gP+9re/xbPPPovnnnsONTU1iIiIwNatW71ek91ux5133oktW7bgxz/+Md58800kJCTgF7/4BRobGxdnw8HY2BgaGxuRmpoKtVqNwUH3nG0gUCqV7KATaaP2dUZICF8iHyKT4yldKEU+DYOGeVUrWKia0f8rz8DLB33//VEn/se7TA7wfPWA22PCnx8RcRIlIFI6QiUA8hxJCV2yIgnvNY3xJG+qu7W4vDTVbZbm/MJ43qZNUnGefH6IdYLF7gLtsGJ0Uo/mniEk2afxmw0q2IKjMGwJYusvYtd6bkECgpUKt/oF19tHSvftrrdb8cDFM2Kd3jrQPmkdx5YiQQcagAuWRuPTDoPoYOflpakoSIpg03eJkaGiqbBLzl2PMMaKldkaHO3TIT3Eigz7AJ77ZBx/OaJ3q8tY7LTb75VmgAkb5SaAmqIORX94sOjxc22bLYQvcz4KhYJNvx09ehR/+MMf8Morr2BsbAzXX389tFot6uvrUVBQ4HEdf11Mf//732Pbtm246667AAAPP/wwPv30U/zxj3/Ec889B4Zh8Mwzz+C+++7D17/+dQDAK6+8guTkZLzzzjs8qwUhtFotPvroI2zcuBEVFRU477zzkJV1ctRgUZEPTdPo6OhAf38/VqxYgdTUVIyNjc2pEjUAGI1GtmHAm2inp7WkIhZu4wJ5H1IQkk/DoAEvVvfh4+axeSWHharlSBGPFCEwkHjCx9eLQYp4bj8vFzESSgCku41slu8JJPeJFL+wPrSrbVKUBL1ZJwDuA4/3bS3AuZkhOD4whvs/H5V8H2Sj59YviNDoSwcGeE0DYrpvJP22c3s5SzxSRPXErm78bnc3qyw9oLNgvLsFFasycf2GXLf6kNj7+tVFBaLt06kxKrxVp8eDu8ZPPB6EG1WReP7whFu0sjpVhczYMNHfXd8URNUVFso2W4hA5nxCQkKQm5uLF198EQzDoLW11es4RiAupgcOHMCdd97Je2zr1q145513AAA9PT3QaDQ8Y7no6GiUl5fjwIEDHsknJSUF//rXv3j2DFxX11NOPhRFgWEY1qWT2BOQyd65tkEAgMOHDyMrKwsFBQUB15CkIh/iIWQ2m31qXOCSz8/easY79e7DlO5wbwxYDCiMC8JxrdMnUvCX/LgNAwoK+PaqeLxW577R+0JKFIAbKzPYTZkbmSgo4PzCBLbdeiZNlC56xyzmhkp+M0KS8RSZAOIDj4/s7MayG0oREp8BBlq3c12RC6zPjUMwZcewzoy02HCkqEMlO8doxrPum3AeRkqglBDAzu3lWJcdg+oh4INWHZ78wn2WRmqQc+f2crdmBrFjucTDPf+nB2qxIikU31+jxl+PGdnz3rw+CX+r8d1mez5ss4UIROGAq2hNUZRP3bCBuJhqNBrR44myNfl/T8eIoa+vD//+97/ZiIooHnA/h1NOPsDMh1ZfX4+kpCQUFxfzLnCuyIemabS3z8gAFBYW8sK/QCAW+RiNRtTW1iIqKspnmRxCYg2DBh+JB1gMxCPsHgPgM/EEkvLjHk8zkCSem5a58Pc2pdvjpHVZQQE3VmXiheoBfmqMAZ78RhHaR6fw9+qT0RrNAC/XDPnVwn1+YTw+bZtkH7tkRRK7wQk7zUh6SGq49JqX6nDHphzRO/ZQlQr3fKYFAy0o9OK7JWE4pyARD344KHmtNCOt+yachyHdcrUDRlHfHJKu0lpoPHmCtMhzZMOXSt+JDX6KDYlKkfkl55YjxGVGglaLnDALBvVW5CZGYtJu9phaWwjbbCECcTI9naV1AOD48eP485//jLvuuktS1fuUk09nZye6urpQVFSEjAz3QmRQUJDPlgpS4A51BgUFuVktBAJh5ENUF7yJm4qtwzAMjvbrZ31Ns4fvEZVkykwEQqKai5Sf1PkLCouwlR7FzuMG9tEN6cEoSIrEjtqZusHz+wfcXs8A0FsceL7aPU3IALi+PAOv1Ihv6goRYuOCmMkJO80e+KCDJUUK4qTMYEYiRjhzc3WxCq83WzjrUXipyQZVkOeBYJLq81XRwOqgJX1zSLpKYxYXNx3QWSRTXWKDn1JDomLzRmmx4QDCkZCQAHWKDVEjekRRVrg0GjfPJrHU2vP7+1Hdo2d/nkvbbN7nQNNgGGZWkY+vCMTFNCUlxePx5P9HR0d55QMy6C8Fs9mMvr4+bNq0CUqlElFRUaw/kFqtRmRk5KknH5VK5TE9xe1QC6TtcHJyEvX19UhMTERxcTG+/PLLOYmkSORDZHJGRkawevVqJCQk+LXOhNmJ5nEH8gvDZ31Ns8f8RFTFqVFoHnGflXE7uw+NBt5w9/+OC94Fhf1DTuwf0nslPymbBgUFXLMuHVuKEvDtl+rcnruxMgPPVw9KEhvNiJvMMeBEQpBuTCAzNzu3l6N+0AgGM0ruYueJSU6HghK2i8+srqCAn23KQnJUiFt9aEhvlayHeEtXJYa5zz2RtnCx13oiOrHzXF6aiguXJ4nO4gjrSbdVJuC7JRRearKyzRD/l+tCX2sdpuPjcWAUeGLPsNtnN5e22bz3dSI74i/5mM1mVg3aVwTiYlpZWYndu3fj9ttvZx/79NNPUVlZCQDIzc1FSkoKdu/ezZKN0WhETU0NfvCDH0heS2lpKe6//36YTCYYDAZMTU1Bq9Wiv78f09PTMJvNp558iK+3FMgvzd+iHcMw6OnpQVdXF5YtW4aMjAx2qHOurBCcTicOHToEmqZRWVmJ8HD/COTNo0P45XutM7WG2npW5oQgNkwBndWFxZBmmw18IR4AuPXcHNG2ailIdcaJRQ/ir/fuagrM3HkDgMVO49oVEXi92eQ2ROqN2MRM5oRgIN2YQGwKuDURsfXEZHi2n52FdJULNvMUJkb78N7ufuSnJSAuLg494048+km3aO1L2LEmbGZoHDbOWDrQNO45Pxe/2d3HS71du6OOJQ+hPI5Yt1tYsMLj0Kfw9yxWI3r2wAR+vzkaOzeuYteIVymg1WrRMTiOJ/ZoJX8Hc2WbzQXZ2/xNu01PT2PJEvc5Mm/w18X0xz/+Mc4991z87ne/w8UXX4w33ngDR44cwd/+9jcAM/Wm22+/HY888ggKCgqQm5uLX/7yl0hLS2MJTgzZ2dl44IEHPF7rKScfbyBzN06n02fycTgcaGxsxNTUFNavX8/zDZ+rGpLJZILVakV8fLxbncoXCIVBSZqCC52VxulOPP5Aini4d9XcDZcBfMrhidWnKAA/3ZiFJ/a4z/+QDZgCcMemHESrgtjuKQrA9aXROGdFNjJjVaJq09w1pN6L2DVJNSYQ8pOSnxF2rkkpGzy4bxg0MxMB/aDMidzJfjzypQVcFWhS+1qVoXYrxEs1M1CgcO8FM9I/XMkgYbGfu56Yvh2XrDxFN96EQcfMDJbh5OcfHByM5ORk9FlCRRs3CLIjXHA4HH6LgHoCt7vLHwTq5eOvi2lVVRVef/113Hfffbj33ntRUFCAd955BytWrGCPufvuu2EymfC9730Per0eZ511Fj7++OOAJM64OOXk4y2VRlEUKIrymTBI0Z944wiF/GZLPmQw9fjx41AoFFixYoVf6cD5FQadPQJpBggE24qT8EmreyeVGK4oTcF/ajUzaSof1va1xrQ6Nx7UHncZnntWK6CZdkIVHo7MECt+8iF/bueVegOuOXsmEnngA/dJb6n5IQYn53qkfHtIUdxgceDpz2bO+8znPdCa3BsSGHiW4SEWDWIRwl+O6PH4ZcvAoM1tTcPYIEaD49E1Goa85GjJjryTr6Hw6119ePwylcdiP3f2hsz+eCIrqWv3JgzaY3DiUR9brQk2ZqsQatJg375uREVFIT4+HnFxcVCr1bPSVgvUSG56enpBXEwB4Morr8SVV14puR5FUXjooYfw0EMPBXQ9Ujjl5OMNJFXmC2EMDg6itbXVY9F/NuTjdDrR1NQEnU6HkpISNDY2+vXFFAqDLkbMF/EISS0sWOkT8VAA/lun8d4+zYk0fHkPDICWkWnR56wx2Xi5tgc0YwXg3k5KMzMacI/t7HQ7F1es89c7u9w2RjLXozHaRH17bj3hc/TM5728TVms447I8IhZNPiibCBl0zBgUuCRf/eydagfrovG/5Vlotcg3fFHvtNSdSOx6CUjxjNZebp20WFXCrh2pRr/qDf61GpNAdhSlIDrKzLYdJvVamX11wYGZqLi2NhYloz8vdsPZMYHmIl8TuduNyHEavaLnnwAz26mAN9qwVvRP1DyMZlMqK2tZQdTSbOBr40QDYMGtr4DLKxg52KA8P1KtZUL26KvW5+OHTVD3tcP4AMVazBgADzzWY/X349Uc8JvL1uGVRnR6Nda3Lq0bj8vF3WDBvZYqU01KSpENMrhdtxRAG6rTERJmlqyGcCbsoFYfUishvWXIwakK41wuWhQoCSHXcW66IRK2uR9eupu4xKnVLQiNuyaGavC/objPrdaiwmJhoWFIS0tDWlpaWAYBlNTU5icnMTIyAja29uhUqlYIoqJifFKLIFGPoF0uy1GkP2RzHMyDMOm/U45+fiycXsiDK7p24YNG7zemQRCPmIyOcQKwtudjcZgxcsH+/Fidb/kMTJmQFHAAxcVoCApAl92TCI+MgTLU6PwMsdxlMDXuRt2bYjbFIgdJ3aIL514CgoY0llx9zttnM08ByvS1GgaNuJpAamJneuJXd2ibdcKCogLD+J3x3H+doTzQ8JIQ0rZQFgfkoo0tBE5ODs7Arcqh/HHg1pwW3YoMLh3yxLRzR0APmkZF11TqrtNmKIT1oe4a3CHXQEgJVwh+tmFBZ+scwjrT1KgKApqtRpqtRq5ublwOBzQ6XTQarVob2+H3W5HdHQ0S0ZcVWqCQGZ8iC/Q6epiSkCIZ//+/YiPj8eyZcvYz4dhmFNPPr5AzM0UOEkKaWlpPite+0M+DMOgo6MDfX19KCkp4fXKk3N5urPhptlkeAfDAEf7DTyfGDFQkNZkEwNp702PDfWq43b7eTk8bTbyvDcNOArAtkwKz+zpYQv4M/WaXrx6Q6mkc6oYiZJ0F/+6+BEJAPy+egzrlnqeHyLX4UnZgEs8UlHSk7t78NQJcth5awF6J6bhtJqgmdBBYZpE7FQnamsnEB8fj/j4eJRlRePteo0oaZD3nRmrwrrsGLdIRCxFt3N7OT5pHfc47AoAsWEUtpfH4U+HtLz3z21mCBTBwcFISkpCUlISGIaB2Wx2M46Li4tjySg4ODjgyOdMSLuRG/O33noLn332Ga688kps3boVa9euBUVRpwf5CAmDSwretNOE8NUKgevvw5X74V4TAMm27fkWBj0TILbJvdsorr7LxczmTIlGDryBz8pMOGgaLx8cwo6aQcmI4vdXFsPmYMCAQWlGNDrHzW6NABsLEkRrOGTGhwHwUb976zbNAG8dcE8FkffxxGXLMDpld9tUyXOkOUEqIvlQRP6GgfiskJSyQdOwETe91uAxSiJrkEijYkk8gHjYbMn44LP9UKYWAbBAp9Ohu7sb064gPHDQXfiTnJPbxk0iEY3Rho9bxiTleDwNu5JIyWJyYtvSGFQWZ3ltZpgNKIpCREQEIiIikJmZCZqmodfrodVq0dfXh+bmZkRFRSEkJIRN0fsTAZ0JaTeyR1511VVgGAbvvPMO3n//fZx77rnYsmXL6UM+pOZjs9lQX18Pm80mSgq+rOWNfAwGA2praxEdHY2qqipRmwWpLjySZnupul8mHi+YTUQoVnOhMEM4z5+QziGq19yoQFgUpxngthMabeR5IUgjgJiC9QsHBr121f2nzSz6OKmTABDdVMlzezom0DdhESXbVw97s9rgrydMc3HrUoB/sjoA8Hb9KB47pgRz7DhLKl8/ewU+bx4Cg16367jt7DSU5yXB6qChMdpERVWFIOdclx0jmqbjtn9TAH5cFYSSXLXXZoa5BFeVGpjZp7RaLQYHBzE9PY29e/fyGhdUKmkxU5fLBYvFctpHPgTr1q3DunXr0NvbizfeeAPvvPMOvvjii1NPPr66mbpcLuh0OtTV1SE2NhZr1qzx2XuHC6VSCZtN2r+DdMzl5eUhNzfX4/UJB1bfPDr0lY925qNV29d6DYMZwvFEBgxmhln/sKdX9Dix15DuNl8UrAHx+pCw/ZsCg2uWKmEY6QUdqsa169Lwj8PD7HzR7efl4qPmMTz1WY/U2/UL3EiDWx8Sa+EmqTivsjpGG369q5eXZiTRxYqcZCgo9/Rl/8AQ/rB3RmFAQQG/2LIE5yxNlCQe4TnFakpcC3AGM4OmrxZmeG1mmE+EhoYiNTUVNpsNKpUK2dnZmJycxOjoKI4fP46wsDBe4wJ3L5uenunCPN1rPgRkdionJwf33HMPbrnlFvzmN7859WZyvkChUGBychJHjhxBbm4uVq1aFRDxANJWCDRNo7m5Ge3t7Vi9erVP+mzcFJ5waPSrivkgnh9uSMXNHOM4T8f6cv5n94jXXzxBzOFULFJSUMC9W92l7xkAv9iWj2+sSsbmpfF44MJ85Gak4vcH9fi/1zrwyqFhXjPBU5/1zBnxAMCgzirqZEpauIXvQcoIjktintqgAYga1L3bd7JbjmaAR3Z24b9fHPNIPELlaa7zqNQ1kGYGqWtfKBA9yaioKOTk5GDNmjU4++yzkZ+fz5YP9u7di2PHjqG3txfHjx/H1NSMIshsIx+tVotrrrkGarUaMTExuPHGG1likzr+1ltvRWFhIVQqFbKysnDbbbfBYDDwjiNZH+6/N954Q3RNhmEQHBwMk8mEXbt24bHHHsOPfvQjfPnll6c+8vEGp9MJvV4Pm82GsrIyNydQfyGWdrNaraitrQXDMKiqqvIYEgvX0hisaNNpUddv+MoTz1xAGCGsTw3Gn/ePiEcYEKhVn0i5SdWB/LkGXyItBQUsTYpA26iJfWxNprsyAAE3Vbjr+KToMfOF56sHsDQ5wmsLt5isDtcIjlgf+Ov5I1W3YkAhPi4eFPizXBSAx76Wh7KcBMnPU2O0QWu2S0Y4Ys0MCw2xhoOgoCAkJiYiMTERAHiNC9deey0mJyehUCjwxhtvYOvWrQG7OF9zzTUYGRnBp59+CofDge985zv43ve+h9dff130+OHhYQwPD+PJJ59EcXEx+vr6cMstt2B4eBj/+c9/eMe+9NJL2LZtG/uzlFgzRVF48MEHUV1djampKVitVqxZswa//OUvQTFMIBMScwupNNj09DRqa2vhcrkQFxfHMyUKFENDQxgaGsL69esBnBQeTUpKQlFRkV+dKY+9sQf/aHPK3WxzBCHxeDt2e3kcpuhg7Dg8yj4mfC0F4N5t3jvViEact864+UgrLhTu25aPx3Z2um3UO7eXY3za5pMRHLcZQUEBWwtjsbNNB7G2G7I2V62AmyIjx7x6Qyk6xky881xfHILV0RaEh4fz0lOkaM+9Lt7vD8Cd56bi+rPcHT+F7qYLgdbWVoSGhvqs02az2fDCCy/ggQcewPLly1FbW4uVK1fiL3/5CyoqKvw6b3FxMQ4fPoyysjIAwMcff4yLLroIg4ODSEtL82mdN998E9deey1MJhObbaIoCm+//bZHbTcutmzZgvz8fGzevBkXX3wxa965aCOf4eFhNDc3Izs7GwqFAmazeNHWX3BVsnt7e9HZ2Ylly5YhM9N7WoeLhkEDXmn1zb/mqw5fN2x/PksGQE2fEYc0DhDakqrxiHXGUZjRbTs+akZCZDDSYsJQN2jEB03jborLgV7jYsMjH3fi7LxY7O/WSRbsuXI0YtI23IYLmgF2tutw92oKrvhcr80JQoUBcgxpg+ZGSSnqUDgcDrQPjKJ2cBJhfSNQB9GIjY2FK1SNBz88qerA4KQmnWu0AxXF8W7vXUofbr7hb5dbaGgoSkpKkJiYiMOHD2NiYgK7du3ye386cOAAYmJiWOIBgM2bN0OhUKCmpgbf+MY3fFrHYDBArVa7lTl+9KMf4aabbsKSJUtwyy234Dvf+Y5kmeKtt97ipRBpml48rdZk+hUAa1EwPDyMVatWISkpCb29vXPqZup0OlFfXw+9Xo9169b57e8jNxbMYD5IxR8c0jjhi1CRlJLB73b3zvk1LXbs7dLh7LxYfKcyU7Rgz20aEEuTCUEzgJ2hcKEPbdDeNN24w6IA8F7zBB78sJsljJ9tykZONIV9x0dF04dxEcEYpWnUDZtRHBThkz7cYnQxJaKiFEUhMTERV199td/n1Wg0bpYMZA7JkwMpFxMTE3j44Yfxve99j/f4Qw89hE2bNiE8PByffPIJfvjDH2J6ehq33Xab6DrC2hUh40XVcGCxWFBTUwO9Xo+qqir2w/Mmr+MPbDYbzGYz7HY7qqqq/CYeeX7nJOTP4PTE3i4d67XjqWmA1HQ8QUEByRFKyeaE6m4ttv6xBje+1oCtf6zBW3UjsNjd539IlEQgRhiPf9aP0NgUnF++yu26KDD45Egb7j3owo//182eC5BujBCqyM8HZmuhLcQ999wjWvDn/pOyzPYHRqMRF198MYqLi92sEX75y19iw4YNWL16NX72s5/h7rvvxhNPPOH3ORZF5AOctNJOTk52q71IKRz4i9HRUbS2tkKhUKCsrMxv2Qs54plbnM71k9MdHzaNwWKnPTYNiNV4hD/feU4q4oNnbAq8tUH7o+nmiTDE5n1+eFYm/rRv0K3tu1BNIz0m5pS1XQdCPp4UrX/yk5/ghhtu8Pj6JUuWICUlBWNj/NEAp9MJrVYr6WpKMDU1hW3btiEqKgpvv/22V4uJ8vJyPPzww7DZbGw9xxeccvJhGAZdXV0erbTnwgaBKCLk5+ejs7PTb+LRGKy4/z2ZeOYKCgrYsiwBH7dOnOpL+Uri1cPDePXwsFdFAzFvoKvK0tjmhJRgG3p79bzXkRYmb23QUs6ogLigqIICJk12aIw2N6Lr11rAMO7uqEfa+5AVdhzXL1dhR5OdbY9fqLbrQFStPXn5cLvkPKGyshJ6vR5Hjx7F2rVrAQCfffYZaJpGeXm55OuMRiO2bt2K0NBQvPvuuz6peJPZS3+IB1gE5EOKVOXl5VCrxV0EZ0M+RCbHarWisrISCoUCx48f90mNmnjvhAcrcbRfL3e1zSFoBjLxYP6jP2+CqIRg/nF9KeoGxRUNuN5AwsL9HWclY0U4Jfrc7efl+N0GLSUoSt7HXW+38RoGuAQidq6tG9YiOpjGu/9rBYMZMWAGwGeN/ahKoRAXF+fm+TWXCERYdC6kdYqKirBt2zbcfPPNeO655+BwOLB9+3ZcddVVbKfb0NAQzj//fLzyyitYv349jEYjtmzZArPZjFdffRVGoxFGoxHADOkplUq89957GB0dRUVFBcLCwvDpp5/isccew09/+lO/r/GUkw8A5Ofne7S2DgoKCqjmw5XJqaysRFBQEGw2Gyvt7Yl8ZFFQGQuB+f56MYxvBHS0rgGFaXEe01NidZin943iyXNVos8983mvm62EMOLgXpeUoGj9oBF3vd3q1qDAbRhIUYfil9vy8dBHHWBAsS3zANCpc2BXF3+48ot+G85q7EWSsoU1j4uPj0dUVJTfZOEJc5128wevvfYatm/fjvPPPx8KhQJXXHEFnn32WfZ5h8OB9vZ2tpP42LFjqKmpATCzJ3PR09ODnJwcBAcH409/+hPuuOMOMAyD/Px8PPXUU7j55pv9vr5FQT7eIpBAIh8pmRzyRfB0RyI3Fcg4k8CcaEOu6dXhzVr3TicFBVQsz4PSPoVrlirwaruL3cDvOT8byVEzkYFUGm3cIv3cirQoVieOO0MkFiVx1cS5HXCx4cEeGxRIpPT1kkQoRtvQHZSFVw4NY0fNIF45NIgLCsX9vRzqDGwoTWQHPBsaGsAwDKvRFh8f73cqSYi5bjjwB3FxcZIDpQCQk5MD7pjnxo0b4W3sc9u2bbzh0tlgUZCPN3Bnc7wRFU3TaGlpwejoKNasWYP4eH7PP5d8hIU0WRRUxpmKo/16UeIh9Y+inFQAqbiroABXjhnQ0j8GlXMaCksPDhwYmokKQtVukREFIExJSdZomoaNLKmQaKZqSZx7BCViOUEIxtPaXDXue7fkIhiY0cjjrPFJm3h6tzRTzWqwpaam8szjhoeH0d7ezg65xsfHIzo62u+oKNCajz9K/acrFlWrtRS4hOEJpFV7amoKVVVVbsQDzERZYrYKbx4dwsan9uFFmXhkLALkxvvXiXXbxmyPz//zqLhzLIMZDyUCiqKQmxyDi9ctxabKNVi6aj2GFMmoHrCiu7sb31pC8zYNBsAD1WZUd2tFtdzEopm6QYPPOnlSGnNiaz/2SQ96pinRtauWxPAeu7QkiafkQN47MY4rKyvDWWedhZycHDgcDjQ3N2Pv3r1oaGjA4OAgLBbvbdrE6TiQyOdMUbT2hEUR+XiLZsh0LRHpE4M/MjnCNJ4sCipjsaFn0n1zu3h5ItJiwvD3/QNuz/3hiz7Jtbw1NbzbOIYLihIQHhzEk555q26EZ+xHAbj3glw8tdSO2z86SWYMZkjlox+UedVyI3I4YpGMp/qQWHeb6NqUe+u4ggIevLgQ49M21A0YUSqQEJJCcHAwkpOTkZyczLqLTk5OYmxsDB0dHVCpVGx6TsxSm+wxgTQcyOSzSCDlnQOAJ5Mj1aothJB8Pmsfl4lHxqJHVqwKz+0Xt2P3lKr35bt96wlPI25qTOgoywD49a4+PH7ZMgD8SIpmgPe/qMG67Bgkx8cjShmMzNgwUSJIiwkTbbW+vDQVFy5P8igESt6nVCouP4aSbONOUYf6RDpioCgKkZGRiIyMRHZ2NpxOp5uldkxMDEtG4eHhbBOVHPmI47QhH7GmA6fTicbGRhgMBqxfvx7R0dE+rUfSbqTG82K1+B+0DBlzB7HEkn9oH5v2SDJzAZIae/yyZZLeRlKRywWVqxFkn0LH4Dg+PtaNdHUwvr9Gjb8eM/qk5UYg9h7FOuGEJHP3eRmIp0ewQRAlzcc8D1eZmmEYWCwWTE5OspbawcHBiI6OZm+a/bGAkclnAeGLoZxQYocoXoeFhaGqqsqvXn2lUol3mybwxJ46uZVaxgKB+x1nUJpAoc7PMafPjmvn9IqkQDOAweKUtCkXc0T91UUFyE2OwVt1Fjz4+TRoRgEF5cL31wI/W6PEr4+e1OGT0nKTEv+U0mbbub2cR2AhThPa22cUzrmeQ9yf5wMURSE8PBzh4eHIzMyEy+WCXq+HRqMBwzDYu3cvoqOj2agoMjLS4553Jlho+4LTouEA4EvsaDQaHDhwAElJSSgrK/N7SKzPyOC3nw9+JYmHAnD3Bflej5Mxn/CfePxbHXjoEndLAX/w6Med+FpJEo8yKU4K6/LSVOzcXo6Hz4vHXy5MkCSJvx41Ii6rAMKoj2aA/fXHMTExMZOFkCAYMnTqSZuNREpcBem36kbcNOUWCkqlEvHx8UhPT0doaCgqKiqQnJyMqakpHDt2DPv370dLSws0Gg3sdjvvtaS2dKa4mHrCooh8fAGJfNrb2zEwMICVK1f6bbLEptkOWufpKk8NFBRwWS7wVjc/taOggEtXpuJ/9SNs0ufhS4tw5dp0XFySgj6tGS3DRhzu00OtCsI7dRq59nUagYK4VxEDYFgvbRXvCxjMKB+89p1SDOutACisyuAb5aWoQ7E8MYSdDfG3wSAtKggdHR2wWq0YdkVKEoyvrdZ3nJWC5SqFKJE98EEH4iKCsbFAfOZnPkBmfFQqFdLT05Geng6apmEwGKDVatHf34+Wlhao1WrExcWBoihkZGTAbDYjPDx81ucnzqTvvfceO2T6+9//3mNKb+PGjfjiiy94j33/+9/Hc889x/7c39+PH/zgB/j8888RGRmJ66+/Hr/+9a/9dpdeFOTjS9qNoih0dnaCYRhUVFT4nRN98+gQfvle67znzD1j9nl/BQV876wc/HXvzFyEggKuymNw1fosrIrpQU7JeoSHKGFxuJAdF46U6DDccX4e+rRm9mcASIkOQ0p0GMpz4/CdDTNrX708Cl80D2CMicbnbaOYmN3+JWMeQYHBL7YsQbJEOum5fbOvYxJpna3FJ6X5hYZsDMOw0YYqROGWqvOUpqs84adjNpvR3j8KqobvQktRQIjC3QdI2BlHrvXpfRo8ea4KjKhj6kxTxaUlSXj00mWz/mx8gdiMj0KhQGxsLGJjY5GXlwebzQatVovJyUnce++9OHLkCMxmMz799FNkZGT4bPomBn+dTAluvvlmPPTQQ+zPXCJ0uVy4+OKLkZKSgurqaoyMjOC6665DcHAwHnvsMb+ub1E4mTIM4xZ+cmEwGFBTU4PIyEisX7/eb4bVGKzY+NS+0+quXkEBf75qFf7XMIKPmsfYxx762kzkMqK3oLqxEy6DBhvXr0JMTAw+++wzXHDBBX531xBoNBp0dHTA4XAgJSUF0anZ+EfNIHYccLemliGO75+Vhb/OwcbvCd9drYbSrEU3k4jdx3V+vdYfS3GhE6lYTaY4zIDg4GDUT4Xzog3yeq5pm8Zo86jlxjW1I6DA4LslYbi8NBWukCiMW4GsuHD0ay248bUGt2v+ebkKm9avdHNM5eL175QG3PXmDzQaDYaGhlhhT29wOp34/PPPccUVV2DNmjWoq6vDihUr8OCDD/rsGkoQqJPpxo0bUVpaimeeeUb0+Y8++giXXHIJhoeH2czTc889h5/97GcYHx/3qwSy6Gs+AwMDOHToECIiIpCSkuI38QDAsX79otg8FRTw3NWrcOFyvskTBWBDmpI3RPfQ14pw3rJEPPN/K/HFnWfhlRvW4PM7zsKVa9PhdDqh6WlDAq3FhedWICkpib379KSR5w06nQ4mkwl5eXkoKipCclQo7tyUi10/rsBTVxSjKPl0K4LO/299a1EC7/dmd/p3Tn/jYArAsSEz/t6u9Jt4AOCK0lRIJRqKUyLc/Hi8GbJNmJyYtLhESGPGHpvrFpqiDsW67BgemXHrMjjxGn5rBoWXmmzoHJpAX1s9nMOtMIz0IgoWN08fBQWkRgWzkZLUZ1s3YPThk5o9/JXWCQoKYolq9+7dGBsbw7333ousrCy/z+3NydQTXnvtNSQkJGDFihX4+c9/znORPnDgAEpKSnglj61bt8JoNKK5udmva1wUaTcxuFwutLa2YmxsDGvWrMHw8HDAG6ve7Jjjq+NDLNVw93kZaO8exDu9YNNjhFDOW5aIewxW1A7oAQCZ4U4YRvrw2FVr3dJjwMkUGTCj4nDs2DEEBwejsrKSvdMgqctAAlliOTE4OIiwsDC2Y4cUcFOjVUiNVmHb8mQ0DhlwbMCA46PTeLt+NIBPayExuxSnN1yzLg3/PDLM25BfOug+AOoJj1xaiF+82y75vPC7xQCoG/PNwVVsrTdr3QvvFIBLVyZhaWIkripTYsrq4umwAdL1nOEpJ8IcQaJpLquDdkvTETQOG3lzRJ5avGkGiEpbgjUZUexsjX6kF99aQuNfXQrQOFH3XKZmb8IuL01FXEQwO7/ERWnm/Ec9QOAupgAQERGB4OBgfOtb3wro3IE6mX77299GdnY20tLS0NDQgJ/97Gdob2/HW2+9xa4rrLWTn311SGWvx6+j5wnCmo/FYkFtbS0oikJVVRXCwsIwOjoasJtpTIRnMyTRa4Jv980UGPzrpnWwOmmogpUw211QmCdhGOnF1q3LcXtEnCShXBg9Y+o0MTEB3RDNIxkx6HQ61NbWsoZ73MnpQCMfp9OJhoYGTE9PY9myZTzLcoVC4fa7KUmPRkn6zDzVrectwf3vtWJfl96vc54pmLK6fE5h/eCcbPzlS3cVgr2dntun5zJ2E1uLAlCUEoH/NYwBOGk+xh027ddaRE3nFBRgsLoQGyX+nLAhgKTghMoJBJ6aEzJjVTNNRyFR0IcEIXd5NlatcuHC/lG8cUyDD3vseKvViLdbgZ/YOnBt5RJsLEjApSVJeLfx5PsSk9WZLwQqKqpSqSRfd8899+Dxxx/3uEZra6tf5+SCa5ldUlKC1NRUnH/++ejq6kJeXl7A64phUZAPMENADMOwjqYpKSm8DXY2VtprMmMkyURqluFfN62DxeGCKliJj5tH8dKBftZXBMzJaOb/cmksT41kW8Gbmpqg1Wp5Q6+eCAWY2eS9kQZR6S4sLBQNw4kKhD/kw42iysvLMT09DbPZjLq6OnaAzpOZVIo6DH+7ZjU0RivqBgz4y54udEx+dboU3m30LfKjAESFim8mO1vG5/CK3HFZLoV3emhIRUoMgBaNye1x0iFGnSACoekcsWl49qgJFGXC1wQOp2INAQ9+2IGCpAg8+KE78QCemxNS1KGiNaeqJWn4+K0B9v0xAJ76YgRR04PITY7B90vjcdnyZWidsGF1ZvSCEQ8QmKjo9PQ0IiIiJJuwFsLJlAtiPNfZ2Ym8vDykpKTg0KFDvGNGR0/MVvmxLrCIyIdhGHR3d0s6mhIvnkCQEh2Ghy8tctNvI6kwg8WBJz/t5KXHVmacVEtYmRGN6yqy2AgGAPq0ZmTEhKKxZi9ommajNYVCgaqqKr+k2D2RD03TaG9vx/DwsKhKt6/rCKHX63Hs2DFWCw8AoqKiUFFRgYmJCWg0GrS3tyMiIoIlIrVaLfpHkaIOw3L1OG5bZsGr/ZGoGTC7HXN6YfZdicLVfvtpt+Rzs0VlbjS+tToFt7/lnr5bXrgE7/R0ibzKOxhwZmiYk66mw3obz1+HYdwdT6XSdLUDRtFokUsyQh23FHWoZM3p8cuWuZ8HQGJuERLCHZicnIRJr0d+SAhCpswYH7chNjY2oNqxv5gPI7n5djIVoq6uDgBYle3Kyko8+uijGBsbY9N6n376KdRqNYqLi31eF1gk5EPTNGpraz3K5MzGzZRhGJTF2fHQOgbhSVkIUQKjEzpcUFHKRiWXnJh7EabHCIQpsZToMDAMg0bM9NO3tLQgKSkJxcXFfn/hpEjD4XCgrq4ONpsNlZWVXnv/fSWf4eFhNDc3o6CgAFlZWaBpmq3vEP0qouY7MTGBiYkJHDt2DAqFAgkJCUhMTERcXByCgoLAMAza29uh0Wiwdu1anH9+DFsXqh8wnKZupfNbKxKeabYE9M016XBK/N7bRqZmufpJkNZrKX8druMpIJ4+y4pz13sjzQncqIRosRH4O0NUkBqLFHUoT3FgcnISnZ2dsFqtiImJYa0SwsPDfRr38Bcul8tvPyBCPrO9nkCcTLu6uvD666/joosuQnx8PBoaGnDHHXfgnHPOwcqVKwEAW7ZsQXFxMf7f//t/+O1vfwuNRoP77rsPP/rRj04/G21gZtNMTEzE8uXLJVv1Ak27kVSYTqfD1rNniG1oaAgxLoNkUd9XkFRXQ0MDli1bhszMzIC+NGKkMT09jWPHjiEiIgIVFRU+3amR1KUUGIZBZ2cn+vr6UFpaivj4eB7xCK89ODiY9TqhaRp6vR4TExPo6OiAxWJBbGwsbDYbezelUs3YALB1oQrgbqMV/6gZxEsH/CvEfxVAAVifE42aXoPb44DvpPST/7a4dX4RvFU/5vZYVmwoBvU2j/UqsWvguppK1WWkbLCBmeN//GYLL31HIh5v6TB/Z4hS1KFoHDaitt+I1VlqlKTFs1kDs9mMyclJTE5Ooru7GyEhIYiPj0dcXNycRkWn0kgO8N/JNCQkBLt27cIzzzwDk8mEzMxMXHHFFbjvvvvY1yiVSrz//vv4wQ9+gMrKSkREROD666/nzQX5ikUx5wPMfBCe7tpHRkbQ19eHiooKn9c0m82ora1FUFAQSktLWWbWaDTo6elBZWVlwNdL0zRaW1sxMDCAFStW+KSm7ek69+7di61btwIAxsfHUV9fj8zMTCxdutRnQtuzZw9WrVqF2NhYt+dcLhcaGhpgNBqxZs0aREREsJEkIVF/oNVq0djYCJqm4XK5EBERwUZFRFCRC43Riut21GJQf2apSwDA+bkqhISGITU2Ai8eGPT5defmx+KLTvd26a1FCdgpETHORaREAfjZ5hz8Zlev6PPXrQhHYYQZLVrgn51waxgAxGd+ALg9VpAUgWteqnMjDW6KTmzmhxv1cM/FXUM4Q/TlsVYsSYpEWXE+fvFum1ujgdhwKTcqmpycnNOoqKGhAXFxcX7tDTt27MDbb7+Nzz77LKBznk5YFJGPL/A37UYaF1JTU7Fs2TJeKmw2KTwAsNlsqKurg9PpREhIyKwVaBUKBRiGgcvlQn9/Pzo7O7F8+XK/p5ul0m5WqxXHjh2DUqlERUUF7/0HQjwGgwGNjY1ISkpCYWEhXC4XJicnMTExweaIuem54OBgpKjD8MltldhzfBw7DgzgUJ/B80lOI+zusQCwAPBv7kaMeADgEwniUVDAzRuy8Ld9szM8ZADERoSyTQNcUACuPXc5UqLDsHFqCquPD+NIjw5pIRZkOgbR3W1BfHw8vrEqBQVJEXh3fzPOLkrD0qw43mCnt9ZpYYrOV1FRco1iabqieCWiI0PQOGzkEQ8w41l0VVmaW4RFdNjmIyoKpOYzV9I6pwNOK/LxJe3GMAx6enrQ1dWF4uJipKeni64VKPkYDAbU1tayA1z79u2bFZEBJ9ukSafcunXrEBMTE9A6QvIxGAw4duwYEhISUFxcDIZhJNNsvmB0dBTNzc3Iy8tDVlYW6wybkpKClJQUMAwDg8GA8fFxdHV1obGxEbGxsSwZbVw6809jtOK7r9SiV3vmRUJiuGtzLg73GbCnw7sytRSxXLAsAX/ff5J4Ao2CFBSwLjcOX1+ZjHcEs1r3bV2C+PCZv7VPOqfx8CckPRaEH8dEYb3KjMHBQVRrgNc7Zs7/744+XLfe6VdNhqTvAOkBVtLmLTVDJAT5Xtf2iw+R1g0Yvab3xNSpA60VBZp2+yrYKQCLiHx8cTP1tsk7nU40NTVBr9d79PcJlHxIoT4vLw+5ubmsz9BsVAXIdQMzdZ7KykqP7c2eIKz5aDQaNDY2Ij8/H9nZ2R7rO95ATPt6enpQUlIi2XFDURRiYmIQExODgoICmM1mTExMYHx8HB0dHQgPD2eJ6P0fluPLzkk88UkXerTebYkXCwLZ9J/Y1TPr837SOuE2cCoWvXgCBeD6iky0aabwPwHxKCjgnKWJUCqVGDFY8PDHnTxC+P3+MezcXo74DBq37jvMGxB9uWbI75oMgSfVailRUWF9KUUdyn639Rbxrlh/h0tnGxXJ5OMZi4Z8vMEbYZjNZhw7dgwhISFe/X2ImZyvYBgGx48fx8DAAEpLS3kbr79rCWE0GnHs2DEAQGlpacDEQ66F+MZ3dXWhp6cHq1atQkJCwqyIh6ZptLS0sFGZP3Lv4eHhyMrKQlZWFpxOJ5ueq6+vB8MwSEhIwPNXZENjD8XOtgm8UjPk79tecHjb6+eiLuPrmhtyY7CvW+/2uNiGXZkbiwM9Orx0YEC0AYRmZoZecxMiMDnt3pBAM0D3mBEAJRqNXLwkBB9120CDgoIC7jw7FQnhStHWaS6kCGbSZEdmrEqUvLg6cOSxbJrGpMWFF0Te2wXL4mc94+NvVCSTj2ecduTDMIzb5jk+Po6GhgakpaWhsLDQa56VRCtiawnhcDhQX18Pi8UiqqY9m8iHRCZLlixBR0fHrNsrFQoFnE4n6uvrodfrUV5ejsjISI+KBd5gt9tRX1/PdrT5207JRVBQEJKTk5GcnMym5yYmJtDb2wuTyYTN8TGIrUzAHw5OnNZeS/5c+rJoGm0G73UBqTXFiAcA7ttWgIc/4svX7O/2XpN66KMOADNkJxbJ6K0upKpDRMni9otX49tGK6o7NMhSORGHSezdO4iYmBgwYdGwUOFgYk7eXEl1xpFo7q6321hi4ZrGARCtL/327DBQQeKqE1eXuaffZwNfoiK73Y6pqSlERUX5XCsymUyIi4ub02tdrFg05ONtUyR3EFxLWm59x58CvVKpBMMwXslH2O4cHOwu0xNI5ENannt7e7Fq1SokJSWhu7t71uk7AOjq6mINrIKDg2fVWGAymVBbW4uoqCisWLEiYLVsMXDTc/n5+bBYLJiYmMA6xTgeWEtj31gQPumf/eex2NEuQTz+qE8LU2+KEz/PtimBW68h5/jZ/467qR0oKOAXW5bgy+PjePSTbl40sm1lNP5Z04vfVw+ya95SpkZkRCR+9+Uw79id28tRP2jkDbCKuZ4e6tWLRmWaaRfWZ7nPEQlrTPMBsaiooaEBAwMD6Orq8rlWJEc+ixCEcAj5OJ1ONDY2ehxMlQKXyKSipLGxMTQ0NCArKwsFBQWSXxZ/Ix9y3UajERUVFWwKyx91AjEYjUYYDAZERUWxSrYul4ttCPAXWq0W9fX1yMjIQH5+/rwM4XGhUqmQmZmJzMxMrHK5cM7kJK7oH8V/Giawa3Ah9KkXFiSqEHtfFPwgHgA/OX8JntrdzYsEHt3ZMetrZAD83+pUlOfG4if/beERwvtNY/jZGiWy85YiPyUatMuFbX8+7BaNLIkrwbMHTtaqGADPHTECMIoSjNQA64DOwqbrpNJ0iWGMqPePsMY031AqlYiLiwPDMFizZg0YhvG5VvRVcTEFTiPyISkjl8vF3pH7Ut8RA5d8hNEMkfnp7u7GihUrWFkJT9flK2kQLbWgoCCeIrW/6wgxOjqKhoYGqFQqVl9pNh1tg4ODaG9vR1FR0azMrAKFUqlEUlISkpKScNZaBp1DE9hxoA9vt87dtP5cIpAaj6fj/VnrO5WZiFYFi0YCc4F/HRvB+txYUULILSjEWUtnFI1renQScjoG0fqQEDQD7Nx/FIXp8X4PsCoo4Lr1GaDpYSgUCq81poUA+VtWKpUICQnxWiuy2WwICQnB9PT0KXEx7e3tRW5uruhz//73v3HllVcCEM9Q/fOf/8RVV13l9zUuGvLxZZNUKpWYmJjA8ePHkZGRgaVLlwZ0V0+iAWG6jNstV15eDrXae4HS1845T4rUQODpO0KUK1euxMjICDusG2hHW0dHB4aHh7F69epFkXumKAoFGYl49MpE3Gq04gev16N9bHFpx61MV6N+aGE8YrigAGRHOHD/e9KWDL6uQ1HShDUwaRYlhPyUaGiMVvRNWhAuoXq9JClKVE4HIqnCssJsKGxGfLuAwuvHabZx4d4tuaINBju3l+O1w4N4+eAQdtQMggJwT4QO366IdpPnWWhwyYcLqVrRyy+/jGeeeQY0TbN6ips2bQo4Beevi2lmZiZGRvh2G3/729/wxBNP4MILL+Q9/tJLL2Hbtm3sz4GMhQCLSOGApmk4HNK+OwzDYPfu3aBpGitWrJj1Hfnu3buxbt06lmC4agirV6/2OZpqbm5GUFAQCgsLJY/xpkgNAPv27UNhYaFPooHATNTW3NwMrVaL1atXIyoqCj09Pejs7IRKpWIFCGNiYnwiIZfLhcbGRphMJpSWls6ZxMd84Pefdc27W+hixXx00gHA/RcWoG7QKKrU/cNzspEYGYyHP+xkvXMevGTm+/6r99tZQrh0ZTLebRh1IyDu4woK+OW2fDAMjUd2nqwP3bc1D1esnskyUBSF7hEtWgbGEeowYnrahAeOKkVVEq7dUed2Pq776qmC1WpFdXU1zjvvPJ9vAqenp7F27VqUlZWhtbUV/f39uPvuu/Hwww/7de5AXUyFWL36/7d33vFNlW0f/yXde7e0pbulpXSkgz0ERXZpcQH6yFJUHA+iKOojggMBB27xBQc+A1GgDEGGAmXIENqmdNAWSvdI0t2m2TnvH/U+Jm3aZjapnO/n4/s+zTi5E5Jzneu+ftfvSkJycjK++eYb+jYWi4UDBw7oPFlVExaT+fQHqZMoFAqjbQWpZixNTU3gcrka3RAGwhyO1BKJBLm5uaAoSk1YEBwcjMDAQDQ3N9NyZuAvtwEvLy+NqhuxWAwulwtra2uMGTNGo7DCklh9dwQeSgnAZ8fzcbCk9ziAvyu69vTMHOGGX2+29c460DuAvX3sJp6YpPnCKNrHAS4dlfh4uiuch4XCyc4aNS1ivHSgSK3Gc/g6D58vjMMzewrU6jmHr/Pww4pkiGTKP3tyuhVvI/3dkF3VgsQAF4zyd6b73VgsVvcFlK8vQr3CUMZvB5WtPqNGSQHnimr67A8yd/Ah9WRddh+IoejatWsxZcoU3Lp1S22KqLYMNMV0wYIFAx4jOzsbXC4XX3zxRa/7nnnmGTz++OMIDw/HU089heXLl+u1vW8xwac/9Udubi7s7Ozg5ORkkNRXFSJLrqysRGlpKW0MqitWVlaQSqW9bjeVI3VHRweys7Ph4eGBUaNGAfgrxWez2WCz2b3kzKpuA56envDx8YG3tzccHBzQ3t4OLpcLLy8vjduBlohCoQC/ohRzh8uwcioHz/xUjIoWy3JKYAGI8XPCDV7P4Eg0X7rzYJI/fsrpPYlUE+/P8MGB/CYoqb9eb1yIKzZlxOKzrPJezgYUgJ2/V2n0lXt+fzFWcpzwz3lJOJDXgA1HrmvcolNSQGWzSGN9SCRTYkzoX56D+3Pr1LKmDXNGYEGiH5RKJTK59WpZ0T/vCtG4peeNDrBAgVL5PAdD2aYN+szyAdTtdSIjI/V6bX2nmKryzTffYOTIkZgwYYLa7W+99RbuvvtuODo64uTJk3j66afR2dmJf/7znzqv02KCjyaI4iwoKAhRUVG4evWq3gPlesJms1FRUYGOjg6kpqZqNOPUBk1qN30cqbUJPnw+H3l5eQgPD0dYWJhar5Km4K3JbUAgEIDH46GkpAR2dnaQSCQG1c8GG6lUSvvHjR49Gra2tvjluW7PuO8uVeOqBXjGJQa4IK+uQ0PgAfQNPE9OCoaLvXY/14eS/eHk6YWL9QK117tc2YbM03/gYH4fmToFLB49HOmJw/D0ngL6dgrA13lC3JPSQQcMTbBZQHKQWx+jFFTtdMRqx+lWu5ViclT3zgAJPOS+T89W4rkpwfjsXNVfW3ezI/FAUgDgXo13T5b/aeVDYXEkCy21t8EWe9FjP8yBPg2mQP9qN1NPMSWIRCLs3r0b69ev73Wf6m1JSUkQCoV4//33/z7BR7VDX1Vxpo3FjjaIxWKIRCIoFAp6TLe+9BQK6OtI3V/wIdY2t27dQnx8PPz8/NQabrV9DUdHR4SEhCA4OBi3b99GeXk53NzcUF9fDz6fr2YGasyeHmNBXCw09R2pesa9cbgYF7RoqDQVeXW6qfKmRnnCzpqt0cmaBeDF6eEYHeKORd/kaHW8n3Lq+8iQWLglcQGgOUCzADjYsEFRvU8LSgrI0aBcI5A6UHygG96cF62W1bw5L5reagOAyibNdjpVzSJQVG/hg5LqHuh4bFUqPcTRz8UOUqkU93P8MSXSG+WNnWi4mY8poxPQ2tqK8vJyFBYWws3NDV5eXvD29jbZ3B5N6GMqKpVKIZPJ+gw+gzXFdN++fejq6sKSJUsGfOzYsWPx9ttvQyKRDM15PsBf225yuRzXr19HR0dHL8WZoW7UQPcEz9zcXFhZWSEsLMygwEPWRDKQyspK3Lx506iO1EqlEoWFhd0NmH8KJBQKhUFWOcXFxRAIBBg9ejTc3NygVCrR0tICgUCA4uJiSKVSeHl50dtzxtrqNARi6Orv799vUB/mao8d/+DgALcO/zpsmApssMi62awxH2IB+GJRHK5WtmGhloFnIIZ7uwKlmoJP9/bVom9yMDvaVeN2VoiG/hoWgA/vjwUnyI0OMPcnBWBihKeK71r37QMp4xxs2PBxsdN4X5hPt+rL2toaNja2ao3icoUcUmm3WMnd3R2enp504zLprykvL6f7a7y8vODh4WHSCyx9rXUA9KlwG6wppt988w3mz5+v1WtxuVx4eHjodY6wGLUb0F34z83Nhb29PRITE3spzvLz82Fvb4+oqCi9jl9bW4uioiJERUWhqakJ3t7eCAkJMWjNNTU1qKurg4ODAxobG5GUlKSX9JDL5cLNzU1Nay+VSpGbmwuFQkEr8EiA0sexQCaT4fr165DJZH36yFEUBaFQCIFAAIFAgPb2dri6utJffGNMWdQVPp+PgoICREZG9qkW1MRrh4p61TaGGgOp256cpNuIBe3VchRYYPVSmPVUrr05Lxr3JwXQgSXEy0EtyyG3F9a3042w/SnjNKno+rrt/qQA7M2uxZu/lNIO2q/PDEdGQne9g9RAye4E6a9pbGyEVCrt5TpgTOrr61FfX4/k5GStn1NVVYW4uDjIZDKDtwtnz54NHo9HTzFdvnw5UlNTaal1zymmhFu3bmHEiBH45Zdf1OTUAPDzzz+Dx+Nh3LhxsLe3x6+//oq1a9di7dq1ePPNN3Veo8VkPjKZDH/88QcCAwP7vLLVN/NRVZ0lJSXB29sbbW1tRtnCUyqVaGtrg1wuN8iRumfm09HRgZycHLi5uSEuLo5+LfJYXSFSckdHR6Smpvb55WaxWPQo7bCwMEgkEtqV+vbt27Czs1OTcZu6TkTmG8XFxfUqog7Eu+mxWJwaiJzqNoR4OqjVMQabCG9HlDXqrlwaKFD4udjppL/W/kqTpVE4cPg6D7uXJ0Esp+ispqd4gAQG1ds1HUeTMm7DkRL8tno8fls9ns6cAGD6J5fU6kAbjpRghK8THXjIe9t08jYmRXjCx9mGNtMFun8z7u7u8PDwoOufJBCR9gQSiIzxvdZHcECmmBrjN6XrFFPCt99+i+HDh2PGjBm9jmljY4MvvvgCa9asAUVRiIyMxLZt27By5Uq91mhRmU9rays9ilkTpaWlkMlktMpLG4gxpkQiQXJyMn2FU1BQADs7O72zKKDb0ubq1augKArTpk0zKI0vKCiAra0tRowYQdeNQkJCEBERYZAjNdDd4EoG6+lSh+qJQqFAc3MznRUplUq17TljSrSJk3h9fT04HI7ejWyq7M+tw3oDGzIZgBeTrDAxyhfe3t6QWDmqmXwC3QHohxXJWPxtTr9OC+tmRGDrybJet+9awlFTxl0pb8Hy/3B7Pe6l6eF4/7fbvW5/Y3YUFo0eTk/ZJdvi5FRHmszJ/5fL5WhpaaG36ORyOTw8POhgpM8FZVVVFdra2hAfH6/1c65evYrFixejoaFh0HcXzIHFZD5Ad0G8v1hoZWUFsVh7SS3JHlxdXZGUlKR2tW9o/Yg4Uvv5+aG1tdXg/WOynoqKCty8eRNxcXEYNmyYQfUdoHsGEWlwNWTUN1kjyXooikJ7ezsEAgEqKipQWFgId3d3+n5DtjEUCgUKCgrQ0dGBMWPGGG1LhNQiDufV40xpE/JqLdOuBwBWjBuOby9rP5LbELq/Veo1HnJ7T+cDNgsYFxeJxuZmXCgtRItIASWl/ryBxAnkONoo4wAgxEuzl5tzV4PGpO+tYzdxva4d76bH0lkECUDk96T622ez2fRFFNl2bmxsRENDA0pLS+Hk5EQHIldXV60yE31qPnfSFFPAwoJPz2FoPdF2minwV3AICwtDRERErxM3ueLRFVVH6oSEBNjY2KC5eeDplAPBYrEgEAggl8uNIiwgikEyg6i/Bld91+vm5gY3Nzc1V2rVoXEkELm5uWm9fpKpUhSFMWPG6OzbNxDDXO3xxOQwPDE5DPm1xivkG5vvrmgOPKunhuKTrAq9j0vm+ly83QLqz78XRwLuvoH44vc6tcemJ/ohJdi915ZacSuw4RfBn3UWVq8AwALgZavs05lbW2Wcah2p5+NmhtrA1Ra0x1vPlzmYx8Pi1EDEB7p1v+afAYMEhJ5ZUc8G1+DgYISGhkImk6G5uRlNTU3Iz88HRVHw9PSkg1Ff3099gk9nZ6dZaqrmwqKCz0BoI7XuGRz8/Pw0Ps7KygoSieaJh32hyZG6ra3N4FEIUqkUDQ0NUCgUGD9+POzs7AyawUOsd9rb2zF69OhBsWhXdaUmQ+MEAgHdk0MCUX+9F6Qu5ezsbPQRDpqID3TD22nRFrkVp+kajMUCooc562yxwwLwxKRgyBQUvrtUTc/1GeVjgym+Mswen4D0b673et6hPB4ifZzUai1tIpmagzZpYVUNNBSAdUfKMcYXuCoAHTBeuCcccQGuagq4vpRxmupIv60ej+8vVeH7K7U4Vi7DiQoZ3pzHxlOTQ7D9fGWv9edUt9HBpydEiACA3tYm//XMinx8fOim7Y6ODjQ2NtKWWa6urnQgcnFxoX+r+tZ87pRxCsAQCz4DbZWpyrRVxxX0dSxdgkZfjtSGTjIlDalWVlZwd3dXU7TpU3iUSCTgcrlgs9kmyRy0QXVoHBFkkIxILBbD09OT7iki++naSqmNDTn5PfG/PNwSWJZhaU8oCnqJJoh7Qc8ZP4UCGQoFwEneLY3BjgLwQY+aSs+/yePW9xheR6E78Gy91wf8plY4Q4wwWwG8QUEopHC5qQuhXo4Y5mpP/0fQ1IS64UgJ/rMkUW3SLbn984VxGt93cpDmwNOTnoGIoig6EPXMipycnODs7Izw8HBIpVK6TlRdXQ0Wi0UHIplM1m/9WhNEcHCnYFHBR5uBcn1tlana8PQcV9DXsbQNGv05UhsyybSxsRFcLhfBwcGwtrZGa2urQfWdjo4OWncfGxtrciWaNrDZbHh4eMDDwwMjRoygZdwNDQ0oKSmBs7MzHB0dIRAIEBERgdDQ0EFf4zBXexxeNRZZpQKcKBKA1y7B5YrWQV+HKemv/qKPCk8VNgtw62MOj8+wQMwdF0dvy+7LqcXXebf/FHIDL00NxKMTI+gsoaFdjOOFfM0KuUuFGl/D0dYaGYl+arL6jES/PrOeft9LH9tzJCD1zIr8/Pzg7+9PX2Q1NTXRk3nt7e1pF2ttttOY4GPB9BUwiIkmkWlrc9LVNvgM5EjNZrO1moraE+IpN2rUKPj7+6OhoQE3b97E5cuX4evrq3OtRCAQID8/H6GhoQgLC7PYfWMnJyc4OTkhNDQUUqmUVrSx2WxUVVVBJBLR23ODHTxVXRLu/vjSoL72UGJqlCfO3WpW2xJLGkA84ODgABs3H3xz/RYtbKAAfJBVC+fOakQGeOFqsw0++b134AEANoC4YY7Ye7Nd42uoyuqTg9z0Cjya0JQVqQYj1b47V1dXugaak5MDW1tbtLW1oby8HDY2NmoNrpq2npltNwumZ81H1XYmNjYWgYHaz2kfKPho60itabx3fyiVSty4cQM8Hg+pqalwc3ODQqGAl5cX7rrrLlrKnJubS+83D2R5Q3phYmNjtbLPsASII4SqcwNxWbhx4wZkMpmajHswtw+Hudpj7fRwjVtMloqujteGEO3njLM3u0U25DWHudrrZ6sDwDs0BjJlFz6+UKOxlsUG8DjHCQumJAFuDX2+Rnyg8YKOJrTNiohwysPDA4GBgVAqlRoHyHl7e6s1uHZ2djLBx1JRDRikqN7U1KTzGO2ex+oJcaQWi8UDOlKrXhUNhKrTNekSVhUWWFlZqdVKWltb1SxvSJ2EnIyVSiVKS0vB4/GQnJxslF6YwaCnIIJsNZArw+joaHR2dkIgEKC6uhpFRUVwc3NTk3GbOrNbMaHb+eLD325b9AhvFoAZGpyoTcXMkd7d9aM//6bQXXeZGNE9eJAEI9VAOJCtTsxwL1Q2OYJCb4VfRogC4wPtkDqqewpoXwIFc9BXViQUCiEUCmFtbQ2pVAo2mw03Nzc1g19SKyorK0NTUxNOnDiBxsbGfueCacumTZtw9OhRcLlc2NraorW1dcDnUBSFDRs2YOfOnWhtbcXEiROxfft2tT5IXaejDoRFBR9taj4KhQIikYjODCZMmKCXr1BfwUfVkXr8+PEDZjPkyzfQFp5QKER2djacnJwwduxYeiQ4oNkqh81mw9PTE56enhgxYkSvk7GrqytkMhktSda1uGkuSADuT0rNYrHg4uICFxcXhIeHQywW0zLusrKyQXNZWDEhBHPi/FDVLII1lPjHv3srwswNBRgt8KyaEoL/O1/Zb31oTKhHr9dTUgC3ug0bjpT0Ckqq6jhN9jxLx3aPMdHYywNgWqQ7nJ2dcDynDM4oRJhfd8YQ6+2NDgWFK+UtvSx9zAH5DkokEuTn5yMgIADe3t70lrzq9pydnR0CAwPpsdq5ubmQSqW4cOECzp49i6qqKsyZMwezZ8/Wy/5LKpXiwQcfxPjx49UGwfXHe++9h08//RTff/89wsLCsH79esycORNFRUW0KEjX6agDYVEOBwqFot/eG5lMhlOnTsHW1ha+vr4GFdXb2tqQnZ2Nu+++m75NX0fqkydPYsKECX1eAZBhdcOHD0dUVBR9haSvsKC1tZXuhZHL5XRPja+vL1xdXS223kMuGhwdHREfH6+XlFqhUNAy7sbGRiiVSrVheaYYhEeUjlebbLCDO/SH143yd8aNhs5eBqEf3B+L+jaxmpRaEz2l3mwW8K8/1W69HttjO5C4H5wo6h6BQXqNevm3AXgy1RX+w/yx8ehf22yrJ/gi1VOKozea8cMtNv38DXOi8GCKYU3UhtLV1YXs7Gz4+vqqnT96NriqnnJV/ef+8Y9/ICwsDAEBATh69CgUCgUuXLig93p27dqF559/fsDMh6IoBAQE4MUXX8TatWsBdJ8f/fz8sGvXLixatMho01FVsajMZyDIjPGQkBCEh4cbdJJVlUgb6kjdn+KtqqoKJSUlGDlyJAIDAw12LCCBx8/PDyNGjIBSqaSzgpycHK3rRINNe3s7rRiMjo7W+9/OysoKvr6+8PX1pYflNTY2ory8HAUFBfDw8KDfvzGyQeKS4efnh9UTorFoqgTc6jZ8euY2Kpota4Cdttxo6MTKiX8ZkpJ/iRf3F4HNAu6N8cbJG439bjeqZilKCnjn2E2NzaY9L22VFFDbKsauy9UaPd0Or+Tg1JXrGBnkjYiIcNz76WW11/nkIh8/rEjGniOtas/feLQUnlI+ooO6bX8MdavXFZFIpDHwAOq1InKe0NTgWl9fj0mTJuGll17Cyy+/bBTvSW0oLy9HQ0MDpk+fTt/m5uaGsWPH4tKlS1i0aJFRpqP2xKKCT18nJDIGgAQff39/g6/uyRdBoVCgqKiILnzrUzfR1OujKlhQFRYYEngaGhpQVFSk5u7MZrMxbNgwDBs2rNdoBHMW7VUhSrzw8HCEhIQYLTNTHZZHXBaI7xyxRSGBSJ+MsLm5GXl5eQgNDUVoaChYLBaGudpj1ih7zBrlh6xSAc7fasaN+g5wLc6qRzWsqKOkgP+7UNXr0eS+gbbx+urrUW02JU2lPbMoNqv7sZqk1CW1zQD/Ju4a6Y+oqCj8UdGq8XGarHsosNAJe9TX16O4uJj+t/f29tZJNaoPIpEI165dg4+Pz4A7JiQQ9WxwPX/+PHJzc9V2YgbrwpFMN+3ZkO/n50ffZ4zpqD2xqOCjCdI0KZfLMWHCBFy8eNEo00zJPJCrV69CqVQa5EjdM/ORyWTIy8uDWCzGuHHj4ODgYJBjAUVRuH37NqqqqhAfH9/nnA3iUaVatOfz+aiqqkJRUZHRvNd0oaamhpaU9+U2YSyILUpwcDBkMhm9PaeaERKF0UA/bB6Ph8LCQkRHR/epoiTS7KxSgVkdszWj/XdM1333vvp6KAAf3hcLTydbWgzg5mDTS53Wlyy7pboUceHD4eQTiD8qWvsUKPTlCTd2VDiGudpDJpOhsbGR7qMDAG9vb/rf3phbs2KxGNnZ2fD29tYroyeZw+LFi/Hpp5/iqaee0vg4baeYxsTE6PT65sSig097eztycnLg7u6OlJQUWFtbG2WgHADaStzOzg4JCQkGXWWojkMg+76Ojo5aCQsGgmRmra2tSE1N7de1QRXVon1ERATEYjEEAgH4fD5u3rxpcFYwEMTmqLa2FklJSXqPKdcXGxsbtYyQKAdLS0shkUjg6elJv/+eghUSMLUd4zB1hA9G+TujsL7TVG/HiPSdEWnLC/eE9xlAVIfKAd0OEiN8nZBT1Ybk4L+k0D1l2YsjgYTIYOS22WPDD5f7FSj4uNj1K+u2sbGBv7+/WvOn6tYsUU56e3sb5KUmFotx7do1eHp6IiYmRq/jXL16Fffffz/eeecdPPXUU30eQ9sppvpA2jN4PB49NZr8zeFw6McYMh1VExYVfFQ/+Pr6ehQUFCA8PFytvmOM4ENMRwEgJibGaI7Uzc3NyM3NRUBAAKKjo+mUmli360pPk01DJora29vT3mskK+Dz+bS1j2qdyBizTAoLC9HW1qYmpTYXPZWDxGWhrq4OxcXFcHFxoU9GfD4f1dXVOgfMvStHY9OxEvzvat3ADzYDT04KRrSfM7KrWg1eY1yAq1Z9PYBmj7b7kwJoyfTFknrcLq/AXbHD4egdgA3/U5/bc/g6T02g8N3lanx/pZr2ehtIcq3qsBEVFUU7LTQ2NqKsrAy2trb0v70u001JxuPp6YmRI0fqFXhyc3ORkZGB119/Hc8991y/x9B2iqk+hIWFYdiwYTh16hQdbNrb23HlyhWsWrUKgOHTUTVhUWo3iqIgkUhQWlqK6upqJCQk9LryvHjxIj2nXJ/jq5qO5uXlYeLEiQafHK9cuQInJyfU19cjJiYGw4cPN7i+09nZCS6XC1dXV4waNcpk+7+qdSKBQACZTKbWT6TrFgXZclQoFOBwOBYxgrs/pFIpGhsbwefz0djYCIqiMGzYMAQEBMDDw0PnQNzQLga3ug0v7i+ymP6g1GA3TB3hNaCKTRM91WosAE9NDkF8oAscbKzhaMuGSKbsc1x2z5k+bBbw2+rxGOZqj//8XoYtp6poxdrScUH47lJ1rzVsuz8WazOL+jyOvpALRhKMpFIpnRH3J1qQSCS4du0a3N3dERsbq9fvOz8/H3PmzMELL7yA1157zag7D1VVVWhubsbhw4fx/vvv4/z58wCAyMhIWpEbExODzZs300KBrVu3YsuWLWpS6+vXr6tJrQeajqorFpX5yGQyZGdno6urC+PGjdMoXdY389HkSG2MLIqiKIhEIrS3tyM5ORmenp4GB56mpiZcv34dQUFBGsdBGJOedaKOjg4IBAJUVlbSM3qI3c9A6jEipXZwcEBSUpLFKO36w9bWFn5+fhAIBLC3t0dYWBja29tRWFgIuVyucyAmggShVIE3fi6xiAB0raoN16ra9HpuWpQjfi7tUhMWqDpIk2yGDH9TzXQ0uW8rKaCqWYS2tjZsOVVJW+0oKWDXpWqNW3l9CRSqmkUGBZ+e86lIRtyfaEEikSA7Oxtubm56B56ioiKkpaXh2WefNXrgAYA33ngD33//Pf13UlISAODMmTOYOnUqAKCkpARtbX99J15++WUIhUI88cQTaG1txaRJk3D8+HG1ADzQdFRdsajMRyaToaCgAFFRUX3+0LOzs+Hj46PRZ60vVB2pk5KSaNVXVlYWEhMT9a5HyOVy5OXlobm5GSEhIYiMjDSovgMA1dXVKC0txciRI/XSzhsTVfVYS0sL/WP09fVVs48H/pJS+/r6Ijo62iJMTbWBZGpKpRIcDof+bhD7fPL+Ozs71VwWtMmWG9rFOJxXj4/PVJj4XZgGFoAt93hh3ammfh9HshBAfdx1X4/96oFIFNy4iU8Lev8+lo8PwveXq9W26SZGePY6LpsFfL4wDhVNIqQEG99WR1W00NTU/f49PDzQ1tYGd3d3xMfH6/X7Li0txezZs7F06VJs3rzZYnvyBgOLCj4ABpyxw+Vy4ebmhrCwMK2O158j9blz5xAbGwtvb2+d19nV1YWcnBzY2dnBysoKrq6udDeyPoFHdWy0IQHRVJAfI2nutLa2pgMRmTxqbCm1qZFIJMjNzYWtrS0SExP7zdSIYEMgEKC5uRkODg5qLgv9vWfVbGAowQKwbFwQvrvceyusJ7uWcHD2ZpPGbbOe2QwLFFaO8cHXVxs1bqUJOiS9BAo9a0cJga7g1rTTz81I9MO76bF6v9f+oCgKjY2NKCwspJtF9REtlJWVYfbs2XjooYfwwQcfDJkLNFNhccFHKpX2O800Pz8f9vb2ap5DfUEcqUeMGIHg4OBeX5CLFy8iMjJSK0WTKi0tLcjJyYG/vz+io6NRWFiIjo4ODB8+HL6+vjr305AtQZFIBA6HY/GjdJVKJW2A2tDQALlcDjc3NwQFBelVJzIH5OKB7NvrciIgw/JIMAag5rKgyZKpoV2MqmYRiurb8d6vQ8iwFANLsVkAXhnvhi2X2no9lmQoz+wp6OWKoNoHpNHlQEWgAAD5tW3IqWqDq4M1/nW49wDAHx9LNomxqFQqpa2x4uLiIJFI6KyoublZK9FCRUUFZs+ejbS0NHz66ad3fOABhmDwuXHjBlgsVr96dtUGz/5GSF++fBnBwcE6bW/V1taiqKgI0dHRtDdTV1cXeDweBAIBOjo6dKqTiMVi+uqbjOUeCpAx3VVVVRgxYgSdGQiFQqO7DBgbIuEPCAhAVFSUQZkacVkgWVFXV5da0VrT+39w51WzyrJZ6BYSDEYmtnx8EKZEemH5f7i97tu1hINgTwdasQb03rYj2dDvZc0DZo/rZkRg6Tjtt+O1gQQeYgnVM2j0J1ogHoS1tbWYMWMGZsyYge3btzOB508sSnCgDVZWVpDJZH3eT/bwRSLRgI7UugyCI9tiRIbr5eVFCwscHR1pSbhYLAafz6d7SpydnentKWdnZ7UTXVtbG7hcLnx8fBATEzNkvpRKpRJFRUVoaWnBmDFjaGGIqssAn89Xe/8+Pj696kTmoKmpCXl5eQgPDzfK4DpVlwXiWCwQCMDj8ehheSQrIv1U5pRls1lA7DBnFBgY/FZNDsZX56sGyIooxFrz0dnQDhYoWlxA1qGqkKtsEqG5S6pRWEBMSwcKltpOLtUWmUyGnJycPgMP0Ldooa6uDosWLYKdnR3a29sxYcIEfPbZZ0PmNz4YWFzmI5PJ+g0IZWVlEAqFSEhI6HWfqiN1YmLigI7UOTk58PLyGtA5lozn7uzsRHJyMhwdHekenv4UbaROQmS85ErI19cXEokERUVFQ65OIpPJcP36dchkMiQlJfUrpVZ9/01NTbCxsaF/qPrImA2loaEBhYWFgybmUK2TNTU1wcrKig5Enp6eEAhlqGoW4T9XqnGqpP+ivjEI9bQ3mh/do2MC8Z8/anvdrmqvs352JBKcOlFbW4vLfDb23GJB+edj3pgdhYdSh/dSxwHam5aqYuyaD1He2tvbIyEhQa/valFREebNmwd7e3t0dHSAxWJh1qxZePvtt7WuWf+dGXLBp6KiAs3NzUhOTla7nVhp6OJInZeXR9v29wVRytnY2NABTdUeXdugQdJzPp+PhoYGKJVKeHp6Ijg42KIMQPuDbBHa29sjPj5eq+F5BNU6kUAggEKhMLkbtSpk4F5CQoJeAhND6dlPJZVKad89ha0LZm3PNvg1/Fxswe+Qmk3eTRyrSd+PoqMJJSUl8I8YiTaFLeSSLvAaW2ErbYMDJQbl4I7nT3f06iPquSXYV1D6fGEcKptFRp1cCvyV8RAhij6Bp7GxEXPmzMHIkSOxe/du2kbn6NGjWL16tc515r8jQy741NTUoL6+HqNHjwag7kit6zTTgoIC2NnZ9SleUFXKxcTE0LM5AOj1hSRTTBsbGxEREQGhUAg+n08bgPr6+lpswb6jowO5ubnw9vY2eIuQoii0t7fTJ2JSJyJ1MmM6EpPaVE1NDZKSknQeOmgKVLdnBAJBt0y93QHfFUjNtqYFiX44kMcz6Biq2Ud1dTVu3ryJGtsgvHemppeAQCgUYv/VCmw5x+91nPWzIvHO8Vu9HLJZKlmVqhDBmMhkMuTm5tIXm/p8z1taWjBv3jyEhITgp59+Mpuhr6VjccFHLpf32/hZX1+PyspKjBs3jrZxaWxsRFJSks6O1P2JF+rq6lBYWIgRI0YgKChIq222/iC1KLlcDg6HQ59gKYqiDUBJP4mpTsT6QppeVd2djQmpkwgEArS2tvZbJ9MFEuxJpmxum5++IOqp4ioeDha24FTd0KwLEHFAbW0drhVXIn7kCDyxt7RPAYGmJlw2gOUxwDfFvY+/7X5101JjI5fL6X7AgaT3fdHW1oa0tDT4+fkhMzPT4h0+zMmQCz6kkD169Gjk5uZCqVQiOTlZr5N0SUkJ5HI5Ro0aRd9GURRu3ryJqqoqJCYmwtvbm3bR1rdxVCgUgsvlwsnJacAhaqoF+9bWVtp3zNfX1yATRH2pra1FcXExYmNj1UwHTQWxuyF1ElIn8vX11WlqqUKhQH5+Prq6uvT+fpgDhUIBbmkldv1ejtN1LLUivTnp2avTF/fHuiKzqJ22L9X0FE12OeQ1Ns6NRoKPNRZ8V9hrm+3nJzgI8zNN/5sxAk9HRwfS09Ph6uqKw4cPD5nvnLkYcsGHXIUTlZG+EzGB3uIFVQsecqVsaMbT3NyM69evIzAwEJGRkTodQ9V3rKmpCfb29vSJ2NQzSlTHOCQmJsLT09Nkr9UXpE5GsiLVqaXe3t591pzIqG4A4HA4FrmN2Retra3Izc1FaGgo7DyG4e2jRThb1j7wE00ImwWsnR4+YH+SptqMpmP1JSDYdn8sZo3qHrvRs6l0eZw9El2EcHR0pL8Dbm5uRhGtyOVy5Obmgs1mg8Ph6HU+EQqFuO+++2BtbY0jR45YbJZtSVhc8BlolPbt27dRWlqKqKgog6eZlpeXo7W1FUlJSRCLxbTDM4fD0VtYoArJGmJiYnSqRWmCjI8m23NkPo2vr69RnKhVUZVSJyUl9TkefDAhdSLy/lX7aVS3J4kowsHBwaALE3NAZOBRUVEICgqib39gx1UUNQxuX5A2zaWqsFnAtADgVG8BnAaHg256ZjY9jUJJYy7ZZuvZ3EtRFD2nR99aqUKhoOc96Rt4RCIRHnjgAcjlcvzyyy9ajz250xkywYcUjsvLy0FRFGbMmGHwa1VVVUEgECAiIgK5ubnw8fHByJEjDRYWEPfsmpoak2QNZD4NORETJ2pfX1+DlWPEr04mk6nVpiyNrq4u+v23tbXBxcUFbm5u4PF48PLy0tm1wNzw+Xzk5+f3KQPPKhXgRJEAh64bJgowFUnewFsLEpH+dZ5GD7aeDgf9CQiIK3aIV9+1HdUR6kS04u7uTmdFjo6OA14wKhQK5Obmdq9fTyNcsViMRYsWob29HSdOnLAIQctQYUgEH9XtsNjYWGRnZ2PmzJkGbzvV1tbi9u3bEIvFiIqKQnBwMO3dpO82G/E56+joQFJSksnTb2KASU7EQqGQzgh8fX11KniSrIEM2NNFSm1OpFIpqqqqUFFRAQD09iTxXbP0IFRXV4cbN24gPj5+QAnuJ6fLeo3AthR+fCwZP1yrxUEV1VxGoh/SE/w1OhxoEhD0Nf8H6D8okTk9xASX9NT19R1QKBTgcrl0zVifwCORSPCPf/wDPB4Pv/76q8X5MVo6Fnd26XnCV3WkHj9+PH2/QqEw6ORIURT4fD6EQiGSk5O7+y0MHIUgFovB5XJhZWWFMWPGDIrEksViwdXVFa6uroiMjKQzgoaGBpSUlMDV1VVNsNAXRErt5eXVy4DV0mlvb6dtfgIDA+k6UX5+PpRKJX0S6st3zZwQSXJ/NlCqrL47AhVNXThxo3EQVqcbR/N5ONwjMzt8nYfFqYF9Tj0Fut0NCKpOBkqq+++JEZ5q6jgWgLfS1KXWDg4O9LBEskXd2NhIfwdITxUZoU4Cj74Zj0wmw7Jly1BTU4PTp08zgUcPLC7zUSqVtH2OJkdqpVKJkydPYtq0aXrLGIkSqrm5GVZWVpg8ebLBwgJy8vb09LSYLR+JRKLRidnX11dtdDYRcYSEhCAsLGzIuC0Af2UNo0aN6jVgsC/fNSJjN6cMlqIoVFRUoKKiQq82gfzaNuy6VI1jRQLTLNCI7FrCwcG8+l4ZUUqwu1qW098wuRf2F/W6/fTzAw+TI7VCkhV1dnbCysoK1tbWSEhI0GuEvFwux4oVK1BcXIzTp08zDaN6YrHBpz9H6hMnTmDSpEl6bWmpCgtCQkJQUlKCCRMmANBfWECussPCwkzSB2MMSLGWWP0QTyorKytUVVUhNjbW7PODdKWiogK3b99GYmKiVlmDamMnqRORQDSYMnYi56+vr0dycrJBBeqGdjH+c6UGuy5VW8Tgup6Qms+zPxb0Eh1ocjLoeRubBSwbNxzfXqrpdew3Zkdh0ejhWq9FqVQiJycHYrEYjo6O9PYcqRNpY/mkUCjw5JNPIjc3F2fOnNFrojJDNxYXfORyOQoKCvp1pD516hRGjx4NV1dXnY7d1tZG+7mNGjUKQqEQly5dol2ofX19dSqwUxSFqqoqlJWVYdSoUfDz89NpPeaCWN2UlZWhvb2dDkREsGBpW1M9ISfvuro6JCcn6/w9ALrrRCQQNTU1qfnuGUvCqwmKonDjxg00NTUZtfE1q1SAp/cUGOVYhqJJ3abtSUZ1mNxAPD0lBM9O7dsaSxWlUom8vDxIpVIkJyfDxsZGTcrf2NgIuVxOb895e3v32jZXKBR47rnn8PvvvyMrK8tgBeudjsUFHzIrp79ivT4TSBsaGpCfn4+IiAiEhobSwgJyElJt6iSBqL8Tg1KpRHFxMQQCATgczpBSuZDO/6amJnA4HLr+JRAIIBKJ1CTMltahTWTgRCJvjJM3qRGQYARArZ/IWHJtpVJJi1FSUlKMriR87VCR2taWOehL3daTvrIcMkxu0Tc5AwYsbef3KJVKXL9+HRKJhA48PSHCHbI919HRAVdXV9jY2EAqlSIlJQUvvvgiTp06hTNnzgxoRswwMBYXfCiKgkQi6XcL5Pz584iJiYGPj49Wx7t9+zZu376NhIQEevKmpvqOaiBqamqCo6MjHYhUxwEQZ2epVAoOh2ORM2v6gjh0SyQSJCUl9ToBkq0pPp+P9vZ2emKjr6+v2YfcKRQK5OXl0ScRUwRGUiciwVgsFhslGCsUCrUToKnEKOasBbFZwNKxQYgLdMGLGmo0qo7XmgbHvXBPOFZMCMGV8haN6jhVtHWxViqV9KDGlJQUrdsQiOXRkSNH8Nprr4HFYsHKygqffPIJHn74YYttQRhKWGTwkUr7N1i8ePEiwsPDB9xvJbLnlpYWJCcnw9nZWWthgVwuVxuHYGNjQxfqb9++Tc/4sPQtKlWIGk/Vobs/iGCBz+ejubkZTk5OdCAa7Nk8UqkUXC4XbDYbiYmJg+ZaQMxfiQEoUQ/qUieSy+Vq6qrBWPtg14JGB7viWtVftjpA7yZS4njtYMNGl1SJEC8H/FLAw4e/3QaFv4LSxAjPXkPlWABeure7qVxbF2t9A0/PY7zyyiv44YcfMHv2bJw/fx6NjY1YvHgxvv76a52Px/AXFhd8gO6TXn/88ccfCAwM7HfPVSKRICcnBywWCxwOB7a2trRtj67CArI3XFNTg8bGRrDZbPj7+5vEXcBUdHZ20mo8faTUMplMTbCgr+eaPohEIuTm5tJjjM3lWtBTPdizn0jTd0oqlaq5JA/22s1VC+rZRLp0bBAeHTdcbSJpf04HfU0u1SXjKSgogFAoREpKil6ZJkVRePvtt7Fr1y6cOXOGbkAvKChARUUF0tLSdD4mw18MyeCTnZ0NHx8fBAdrHplLxiR7eHjQpqHkbeqraKuvr0dRURGioqLg7OwMPp8PPp9Pz6Uh4xAs0c6lubkZeXl5CA4ONtiSCPhLsEAyAtJLQwQLxvwMyIBAMu3VUpSEmupEqv1EVlZWtLKSGMqa6yLFXLWgN2ZHoaZVjO/+zL608X4DuqXZ1S0irP+5ROP9A9V6jBV4tm7diu3bt+P06dOIj4/X+RgM/WORwUcqlaK/ZXG5XLi5uWmcBsjj8XD9+nWEh4cjLCzM4P4dVYPN+Ph4tUFkqn5jfD4fYrGYnsvj4+NjEYaWJGiaanqnai9Nz89Ak2JIF1paWsDlco0WNE0FRVFobW2lPwOJRAI3Nzd0dnbC09MTcXFxZs+O82vbsP1cBbJuNg/q6+rjEadJmq3KuhkRWDpO84UnyUw6OjqQmpqqd+D56KOPsG3bNpw6dQpJSUk6H4NhYIZk8NE0BI6iKJSXl6OsrAzx8fHw8/Mz2LFAoVCgsLAQbW1tWhlskrk8fD7f7HN5yOdRWVmJhIQErfpgjPGaqoKFjo4OuLu701mRLsIMPp+PgoICjBgxAsOHa9/LYW4oioJAIEBBQQGsrKwgk8ng6uqq1k9kTkgtSFMzpznoq9+nv5NSX5kPRVEoLCxEe3s7UlJS9BKHUBSFzz//HFu2bMGJEycwZswYnY9hTGpra7Fu3TocO3YMXV1diIyMxHfffYfU1FSzrssYDMng03MIHEmzSe+Ei4uLwRmPRCJBXl4eANA1I10QiUR0IGpra6NPQIOhGiMycDJkz1wuu2KxmA5ELS0tWg+JI27gcXFxQ6Z3itDW1obc3FwEBQUhPDxcrZ+I1IlIIDL1WIz+MF8tiKL/L5sFbJgzAjHDnLWSVgN913woiqIl+KmpqXoHnh07dmDjxo04duwY3XxuLoir/LRp07Bq1Sr4+Pjg5s2biIiIQEREhFnXZgwsMvgMNEq7tLQUMpkMo0aNgkQiQW5uLiiKQlJSkkHCAgIpzru7uyM2NtbgGoZUKqUDEVGNkUBkyKROTQwkpTYXMplMbTYRUQ8SwQKLxVKznDHXDCFDILW18PBwjX0gxGWCNDWyWCy6n8jYtTJtGKxaEMlkuoNNFEZ5WaGwkgdReyu6ZEqw7J3xyTVhv8eYFeuD5eOD+sx4SODRt3+Koijs2rULr776Ko4cOYIpU6bofAxj88orr+D333/H+fPnzb0UkzAkg09ZWRk6OzsRHh6O7OxsuLu7Iy4uDiwWy+AZPMSM0FR1hp4nYVtbW/okbOiVMAnENjY2SEhIsIiakyaIepAIFoDupk6ZTIa2tjakpKQMuZkoxGIpOjpaq853MhaDZEUSiYTurvfx8RkUU1qguxZ06gYfVTW1OF5lmlMBC8CH98ci0N2ellj3VLMNtNXWX8ZDRqWnpqbqHXj+97//4cUXX8ShQ4dw991363wMUxAbG4uZM2eipqYGZ8+eRWBgIJ5++mmsXLnS3EszCkMy+FRUVKC+vh6dnZ0ICwtDeHg4vc3GYrH0Lu5WV1ejtLR00EZG91RMsVgsOhBp4zOlCsnWPDw8LMbYVBsoikJLSwtu3LgBkUiklg1YimhjIBoaGlBYWKjR3FQbSK2MBOOOjg66udfUdSKxWIzs7Gy4ubnhN74DdphoXIOqbY4m1Vvv2o+qPq6bnrUeiqJQXFyMpqYmgwLP3r178eyzz2Lfvn2YNWuWzscwFeT9vPDCC3jwwQdx9epVrF69Gl999RWWLl1q5tUZjkUGn/5GaVMUhby8PDQ0NCAxMRHDhg0zWFhAURRKSkrQ0NAADoejs8OwMVAqlWhpaaFrJAqFQmv5srGl1IMJGV4nl8vB4XDUXCaIaIN8DpayhahKTU0NSktLkZCQoKaENARSKyN1IkdHRzoQGbNOJBKJkJ2dTV+wsFgsrNmbb9C4Bu0Ci2aINPvbPsQQS+OdsGxCCP17IIEnJSVFb5eRAwcO4IknnsCPP/6IefPm6XUMU2Fra4vU1FRcvHiRvu2f//wnrl69ikuXLplxZcZhSAUfpVKJwsJC8Hg82NnZYdKkSQYHHjKoTiQSISkpySKsclQl3DweDxKJRK2XSDUbIFJqY4zqHmykUilycnL6dFwQiURqvnvOzs5qvnvmDrIVFRUoLy8Hh8Mx2TwX1TqR6vh0Hx8feHp66l0n6urqQnZ2Nry9vXv1T+XXtuHtX0pRUG/46G42C3ggyR8/5dRr9fj+tt/en+EDD2U7urq6YGdnR1+w6PvZHzlyBMuXL8d///tfLFiwQK9jmJKQkBDce++9ak4K27dvxzvvvIPaWg3zyocYQyb4kE5xhUKB4OBgVFRUYNy4caAoSu/6jkgkApfLha2trcXWSMiWDI/Ho+eREK8xsViM6upqo151DxZdXV3IycmBm5sbRo0aNeA2oVQqVauV2dnZGa1WpitkpHtNTY3ertr6oFon4vP5kEqlagao2taJhEIhsrOz4efnhxEjRvT52RlLEddXQOnpft0fpOZD5NQCgQBOTk5ob2+Hs7Mz/TloO5/n+PHjePTRR/Htt99i4cKFOr2fweLhhx9GdXW1muBgzZo1uHLlilo2NFSxyODTc5R2Z2cnsrOz4erqiri4OHR2duLq1asYNmwYvS2la42jra0NXC4Xvr6+iI6OHjI1EpFIBB6Ph8rKSkilUjg7O9NWP+Y2/tSWjo4O5OTkwM/PD9HR0ToHDk21MmNkA9pAtmj5fD7tF2gOKIpCZ2en2halm5sbLePu67tAfksBAQGIjIwc8LNXHWttTFgAXp8dhbeP3RzwcV8sisPUET70KI2GhgakpqbC0dGRFvCQ0RhWVlZ0IOrru3D69GksWrQIX331FR555BGzZ9B9cfXqVUyYMAFvvvkmHnroIfzxxx9YuXIlduzYgUceecTcyzMYiw8+AoEAeXl5CAkJQUREBJRKZa+OcrlcrpO9C4/HQ2FhISIiInoNqrN0iDuySCTCqFGj0NHR0UvC7efnZxHbUpog9anQ0FCjDN7rmQ3IZDK1bMCY2azqOAdD6gymoK86kerU2o6ODmRnZ2P48OGIiIjQ+rNvaBdj/c/F+L2sxahrfmN2FN45frPPgXLEaPT+pABQFIVbt26hvr6eDjw9Ua2bCgQCSKVSWkHIYrEQEBCAc+fO4cEHH8Qnn3yC5cuXW+RvRJUjR47g1Vdfxc2bNxEWFoYXXniBUbuZEoVCAZlMhsrKSty8eROjRo2Cv78/FApFr222nvURshVB6iOqdQTS9V9RUYH4+HitRjJYEhKJBFwuF1ZWVr2cnVUl3I2NjbCzs4Ofn5/ZmxlV4fF4KCgoMFl9imQDpKdKKBSqjUMwRLBAHJKJX5ilzTlShTiyk34iNpsNd3d3NDU1ITg4GJGRkXodN7+2Dd9dqsaJIoFRnLJZABKHu4Jb007fdlekB2L9XeHjbIup0d4Y5mpPB566ujqkpqZqpf5TddsoKCjAww8/jODgYNTV1WHdunXYuHHjkNnt+LtikcGHNEryeDwkJyfDzc1NY+DpierJh8fj0YPR/Pz84OXlhZs3b6K5udmsXf/6IhQKkZOTA3d39wFrJGRbikh3VSeV6irhNhbV1dW4efPmoAb9rq4uOiMiLhPkc9BFvqxQKMDlciGXy+lG5qGCUqmkFXlWVlagKEqtn0ifzDC/tk1rRwJDyEj0w6b5I1FWVoba2lqtA48mfv75ZyxduhRRUVEoKyvDsGHDMH/+fLz11luDVrNjUMcigw/5sZAOfX2tckjvRENDAzo7O2FlZYXw8HAEBAQMqRMIMdgMCgrSabsE+GsrgmQDFEXRmeFgdNWrGrMmJSWZRcYOqA8KVLW5Ud2W0oRMJkNubi7YbDY4HM6Qmt8EAK2trcjNzUVERASCgoLoizMiXtHXe89UtaCefDjLD44iAVJSUvSur+Xm5mLevHl4/fXX8cILL0AsFuPUqVM4efIkPvroI4t0or8TsMjgo1AoIBaLjeJYIBQKkZubC0dHR3h4eNBDwdzd3emTjyX2jxBIA2N0dLTBBpuqUzqJWkrVgdrYaj/Sfd7Y2GjW4nxPNMmXNTX3kplQ9vb2SEhIGHInqZaWFuTm5iIqKgpBQUG97idSdoFAgJaWFnpYoLaqsYZ2MV4+UIRrlW2megu4PxxYlzFa7+9Ofn4+5syZg7Vr1+KVV16xiO1nhm4sMvjI5XKIxWL6b323iUhxe/jw4WrKHrFYTJ+AW1tbadNPPz8/iykiUxSFyspK3L592yRbVX3VR8hJ2NDMkEyRFQqFFtM/pQlNzb3e3t5wc3NDVVWV1lJwS6OpqQl5eXla2/2oDgskqjFVBWF/7/+T02X4PxM5I3y3eCTGRunuGgEARUVFmD17Np555hls2LCBCTwWhkUGn6VLl6KsrAwZGRmYP38+AgMDdf7i1NTUoKSkZMDidk/TT9LISBRj5oDIeXk8HpKSkgZlT7qrq4v+HNrb22nZrq7bMUD3iSwvLw9KpVIvR3BzQcQrdXV1qK2tpesjRL5sySIDVRobG3H9+nXExMToNcOpZ0CWy+UDKggb2sXIKm3EW7/0L53Whbmxnnj/gUS9nltSUoLZs2dj+fLlePfdd80WeDZu3Ig333xT7bbo6GgUFxebZT2WhEUGn5qaGuzbtw+ZmZm4ePEiUlNTkZ6ejvT0dISEhPT7RSK9AHV1dUhISNDJGVkmk9E/uKamJjg4ONCByNju032hUCiQn5+Prq4us2UMmkYhaOssMNS3qkgPUkBAAAICAujPob29fVDHYuiLQCDA9evX9faZ6wlFUejo6KA/B6FQSFse+fj49Pp+GloLemasJxoEzZg7NgbjovTzVywrK8OsWbOwaNEivP/++2bNWjdu3Ih9+/bht99+o2+ztrYeck3hpsAigw+BoijU19fjwIEDyMzMxLlz55CQkEAHop5NcuTELRQKweFwDMpciFyVSJdtbW3h5+c3YIHaEIiLgyYptbnoGZD7K9QTRd5QMzclkOJ8aGhorym5EolETbDg6OhIZ0Sm+j7oCpGym3IOUl91Il9fX7i4uIDFYhnUF/RULLBsRore2X5FRQVmz56NtLQ0fPrpp2b/Dm7cuBEHDx4El8s16zosEYsOPqpQFIXGxkY6EJ0+fRoxMTF0ILK3t8dTTz2Fl156CVOnTjXqiVuTdJlkRGQWjaEQYQRxcTD3j0YTCoVCLSCTz8HX1xdsNhtcLhcBAQGIioqyiJOxLpAaSV/FeVV6XphYW1vTgchcUnYiTElISBg0KbuquwD5HFQl/YX1HVizrxB1bRKtj7l6ynA8OTVq4AdqoKamBjNnzsSMGTOwfft2i/gNbdy4Ee+//z7c3Nxgb2+P8ePHY/PmzQgO1jwG/E5iyAQfVYgN/+HDh7F//36cOHECSqUSERER2LFjB1JSUkz2xVMqlfQsGj6fT1u7+Pn56X3iaW1tBZfLRWBgoFaWJ5aA6ufA4/Egl8vh6uqK8PBwk1vcGBs+n4/8/Hy9RmmQz4FkRUqlkt6S8vb2HpTPoa6uDsXFxWb1+FP9HAQCARQKBd1PtKegEzsv1Wh1nL5GZA9EfX09Zs2ahcmTJ2Pnzp0W8/07duwYOjs7ER0djfr6erz55puora1FQUHBkOs1NDZDMviocvDgQTz66KOYO3cuJBIJTp48CX9/f6SnpyMjIwNJSUkmDUStra30CZiiKDWbH21el1j9aHPFbYk0NDSgoKAAoaGhUCgUahY3mlwmLA1y4o6Li4Ovr69BxyJSdhKIxGIxrSA01YC42tpalJSUIDExEV5eXkY/vj4Q4QYJREKhEJ8W2eBWa98zuoC+B8YNBI/Hw+zZs5Gamorvv//eYgKPJlpbWxESEoJt27bhscceM/dyzMqQDj55eXmYNGkS/v3vf9OW6J2dnfjll1+wf/9+HDt2DJ6enpg/fz4yMjIwevRok30xyYmHx+PRJ2ASiPq6Aq6srERZWdmQtPoBgKqqKty6dUvtipsUqElm2NXVpaYYsyTlG1m/qU7cpMmZz+fTA+L0VRBqgrhGJCUlmWykgzEgdaIT12vxv6Iu8MV/XZTFuisxPX44Jo4YplfG09jYiDlz5iA2Nha7d++26AsdwujRozF9+nRs3rzZ3EsxK0M6+ADdP8C+Moauri6cOHEC+/fvx9GjR+Hk5IS0tDRkZGRg/PjxJvuikhMwCURisZjOBHx8fGBlZYXS0lJ6eJ2bm+4/OnNCvLZqa2uRlJTU7/p7noAtobmXePxVVlYOmutCT+NPYgLr6+url5KyqqoKZWVlZnWN0AeZTIYLRdU4f6MWAbZiRHnZ0h6Eum5bNzc3Y+7cuQgPD8ePP/5oURc2fdHZ2Yng4GBs3LgR//znP829HLMy5IOPtojFYvz222/IzMzEoUOHYG1tjbS0NCxYsACTJk0ymbJMdR4PkaqS1xqsHh5jolQqcePGDTQ3NyM5OVknRSFp7iVKKRcXFzUJ92BApPj19fVITk42y757z0K9jY0NfWHi7u4+4AmYDLEjvodDDdWtQoqi6O+EUqlU6yfq7+KwtbUVaWlpGDZsGDIzMy22B2vt2rVIS0tDSEgI6urqsGHDBnC5XBQVFQ3J3Q5jcscEH1VkMhnOnDmD/fv34+DBg1AoFJg7dy4yMjIwdepUk32RpVIpsrOzIZfLYWNjQ4+JJidgS/0BEcg4B7FYTPvu6QsZDsfj8dDc3Ez3VKlKdo0NsftpamrSOXCaCoVCoVaoJ3VDHx8fjd57xCdvMIfYGRNSY+NwOGo9eKp1IrJd25cjeXt7OzIyMuDq6orDhw9btD3WokWLcO7cOTQ1NcHHxweTJk3Cpk2bEBERYe6lmZ07MvioIpfLceHCBezduxcHDx6EUCjE3LlzkZ6ejnvuucdoTZ5kcqerqytGjRoFKysriEQiekuqra0Nbm5u9BaEpdnRyGQyuleBw+EYNVMkXms8Hk8tE/D19TWalF2pVKKgoAAdHR1ISUmxyBNWT+89Mj6dZAJVVVWora01W8ZmKPX19bhx40avwKMJ4kguEAjQ2tqK9vZ2XLp0CXPmzMGmTZtgb2+PI0eOWGyzL8PA3PHBRxWFQoFLly5h3759OHDgAFpaWjBr1iykp6djxowZel8pEyl1fz0wEomEPumobkn5+fmZ/QcmFouRk5MDR0dHxMfHm1RNpFQqadNPPp8PAHQgGshjrC9IxiaRSJCcnDwkagNku1a1XsZisRASEoLhw4db3MXJQJDAo4+4QyqV4uLFi9iyZQt+//132NjYYMWKFXjggQcwefJki2jGZtAdJvj0gVKpxNWrV+lAVF9fjxkzZiA9PR2zZ8/W+sqTz+ejoKBAJym1qv1/U1OTWSeUdnZ2Ijc3F15eXoiJiRnUxj0ysZacgFUVhF5eXloJRuRyObhcLiiKMnrGNhhQFEWLUwIDA9HW1qaz5ZG5aWhoQFFRkUGqQrFYjIULF6K9vR1r167Fr7/+ip9//hk2NjaoqKiwiIZSBt1ggo8WKJVKcLlcOhBVVFTgnnvuQXp6OubOndvnpFAi5TWkh6TnhFJ7e3va5sdUtRECydh0HbtsCnpKuEUikdo4CE3ZDLErsrGxQWJiokX3f2iCoigUFxejsbERKSkpdAZMLI+IYMHOzk5NsGBJgYhY/iQmJurdACuRSPDII49AIBDg5MmTtKxcqVSirKwMUVH6OSIwmBcm+OgIRVEoLCykjU+Li4sxbdo0ZGRkYO7cufDy8oJSqcR3332HyMjIAaXIukDsbUhtxNbWlr76NfaobIFAgPz8fERGRlqkFUjPLSki3CDFabJV6OTkhPj4+CF3ZUxRFIqKitDS0oKUlJQ+t9mI9RMJRsRxg4xCMGfAJYHHEMsfmUyGJUuWoLKyEqdOnbKYRloGw2GCjwGQLZH9+/dj//79uH79OiZMmICGhgZ0dHTg999/N5nBI1FJ8Xg8Nb854qtlSCCqq6vDjRs3jOaMbGpIEyOZz+Tk5ES7CwzVwFNYWIi2tjadxBHEcYN8FsRpor9RCKaCWBYZEnjkcjlWrFiB4uJinDlz5o6XJv/dYIKPkaAoCteuXcODDz6IxsZGiEQiTJw4EfPnz0d6ejoCAgJMth1C5q+QQERRlN5F+oqKCty+fdui7Fp0gUzvtLGxgUQioV2XB3MshiEQVV5nZydSUlL0lt9rGhbYMzs0FWSsQ3x8vN7bzQqFAk8++SRyc3Nx5swZi7oI2rJlC1599VWsXr0aH3/8sbmXM2Rhgo+RKC8vx8yZM5GQkIB///vfaGxsxP79+5GZmYlLly5h9OjRtM1PcHCwyU6CxHSVnHQUCoVakb6vbRjV5suh2PwKAG1tbcjNzUVQUBDCw8N7uXCbQsJtTJRKJT3LKSUlxaiqPCLrJ9Jloqb08fEx6nhzEngMGeugUCjw3HPP4ffff0dWVpZWk1gHi6tXr+Khhx6Cq6srpk2bxgQfA2CCj5Goq6vDN998g3/9619qmQZFUairq6NHQZw/fx4JCQnIyMhAenq6SQv5pHGPuCtIpVKNhp9KpRJFRUVobW1FcnKy2aXd+kBGpoeHhyMkJKTX/WSbkpyASW3EEAm3MVEqlcjLyxsUOThRUwoEArUZTT4+PgbVDhsbG5GXl2dQ4FEqlXj++edx+vRpnDlzRuO/pbno7OxEcnIyvvzyS7zzzjvgcDhM8DEAJvgMIsRK5ODBg8jMzMSZM2cQExNDB6KYmBiTBqLOzk46EBG1mLe3NxoaGiCXy5GUlGTxLguaIOKI6Ohora6SVd3ISXaoGpQHu0ivUCiQl5cHmUyG5OTkQa3N9JxVxWaz9QrKZHR3bGys3ltkSqUSL7/8Mo4cOYKsrCyEh4frdRxTsXTpUnh6euKjjz7C1KlTmeBjIEzwMRNke+zQoUPYv38/fvvtN4SHh9OjIEaNGmXSq/HOzk7U19ejqqoKSqUSnp6etIR7KDRhEsgQNX2vtkl2SAKRWCxWc+E2dSBQKBTgcrlQKpVISkoyqyuzalAWCASQy+Vqcva+1kYG8RkaeF5//XXs3bsXWVlZFief3rNnDzZt2oSrV6/C3t6eCT5GgAk+FkJbWxt+/vlnejheYGAgHYg4HI7RA5FIJEJOTg6cnZ0RERFB10ba29vh7u5O2/xYog0NoaamBqWlpUYbotbTVcDU3ntyuRy5ublgsVjgcDgWNQ5Ata+KzORRnU1EPovm5mZwuVyMHDlS50F8qq/11ltv4fvvv0dWVhZiYmKM+VYMprq6Gqmpqfj111+RkJAAAEzwMQJM8LFAOjo61GYSeXt70w7co0ePNjgQdXR0IDc3Fz4+Pr22+ojzNI/HQ1tbG1xdXemMyJIsXYizM4fDMdksm57ee66urnQgMrQuJpPJkJubCysrK3A4HItvgO3q6qIDEfksnJ2dUV9fj5EjRyIgIECv41IUhS1btuCrr77CmTNnEBcXZ+SVG87BgwexYMECtX8jhUIBFosFNpsNiURi8f9+lggTfCycrq4uHD9+nJ5J5OzsTKvmxo8fr/OXvqWlBVwuFyEhIQgLC+u3xiSRSCAQCMDj8WhLFxKIzOUITVEUysrKUFNTM6jOzuSz4PP5Bs/jkclkyMnJGbLOCxKJBJWVlaisrASLxYKjoyOdEbm6umr9WVAUhY8++ggfffQRTp06BQ6HY9qF60lHRwcqKyvVblu+fDliYmKwbt06iwyYQwEm+AwhxGIxfv31V3omka2tLZ0RTZw4ccD6BPGZGzFiBIYPH67TaxNLFx6Pp+Y3p+8wNH2gKAolJSXg8/lITk42qkRYF3paHhF7G22cJqRSKXJycmBvb4+EhASzq+z0gfRSRUdHw8/PjxYsNDY20s3OAw2HoygKn3/+ObZu3YoTJ05g9OjRg/wuDIPZdjMcJvgMUaRSqdpMIqVSiXnz5tEziXqKBkh9xBCfOYJcLlez+SFSXV9fX52ufHVBVQ7en93MYKNJLabqNKF68iXznIg7+FAMPK2trcjJydF4AUOanclnoaoiVDWCpSgKO3bswJtvvoljx45h/Pjx5ngrBsEEH8Nhgs/fALlcjvPnz9MziUQiET2TaNq0aXjrrbcgl8vxr3/9y+j1EXLyJYHI2traJLN4rl+/DpFIhOTkZIuVg6uefPl8PpRKJS1bdnZ2BpfLhYuLi8mVjKaitbUVubm5iIyMHNChXVVFKBAIIBKJcODAAXqI2tatW3HkyBFMmTJlMJbOYIEwwedvhkKhwMWLF2kH7oaGBrBYLLz22mt45plnTNpASmbxqDZy9pUFaAuRIsvl8kHvgTEE1cFwPB4PYrEY9vb2iIiIGBQJt7Fpa2tDTk6OVoFHE0KhEO+99x52796Nuro6xMfHY9myZcjIyLC4fh6GwcHsl19ffPEFQkNDYW9vj7Fjx+KPP/7o9/F79+5FTEwM7O3tER8fj19++WWQVjo0sLKywuTJk/Hee+9h3Lhx8Pf3x6OPPop///vfCA0NxSOPPIK9e/eio6PD6K9NGhRHjRqFKVOm0IXYgoICnDt3DoWFhRAIBFAqlVodTyaTITs7GxRFISUlZUidsFksFtzd3ekTta+vLwICAlBZWYmzZ88iJycHNTU1kEgkZl7pwJDAExERoVfgAQBHR0fExsaira0N//3vf/H000/jxIkTiImJwY4dO4y8YoahgFkznx9//BFLlizBV199hbFjx+Ljjz/G3r17UVJSorEucfHiRUyZMgWbN2/GvHnzsHv3bmzduhU5OTmM4qQHy5cvR1FREY4cOQIfHx8olUrk5ubSoyCqqqowffp0pKenY86cOUYfyaBKz6Fwcrkc3t7e8PPz69NvTiKRqBXmh5oiDOhWKmZnZ8PHxwfR0dH050tky6Svys3Njc4QLaWWRWhvb0d2dnaftkXakpmZiSeffBI//vgj5s2bR9/e1tYGiqLg7u5uhNUyDCXMGnzGjh2L0aNH4/PPPwfQvW0TFBSE5557Dq+88kqvxy9cuBBCoRBHjhyhbxs3bhw4HA6++uqrQVv3UKC8vLxP00iKolBQUEAHotLSUrWZRJ6enib3myPbURKJhA5EpIueNMC6uroO2fqIUChEdnY2/Pz8MGLEiD4/TzI+XSAQoLm52aImlJLAExYWhtDQUL2Pc+TIESxfvhz//e9/sWDBAuMtkGFIY7bgI5VK4ejoiH379iEjI4O+fenSpWhtbcWhQ4d6PSc4OBgvvPACnn/+efq2DRs24ODBg8jLyxuEVf/9IPJlMpMoPz8fU6ZMQXp6OtLS0uDr62tyvzkSiEQiEdzc3NDZ2QkfHx/ExsZanPO0NnR2diI7OxsBAQGIjIzU+j1omlprahVhX3R0dCA7OxuhoaEGBZ7jx4/j0UcfxXfffYeHHnrIeAvUg+3bt2P79u2oqKgAAIwaNQpvvPEGZs+ebdZ13amY7ZKysbERCoWilx+Xn58fGhoaND6noaFBp8czDAyLxUJMTAz+9a9/ITs7Gzdu3MCMGTPwv//9D1FRUZg9eza2b9+O2tpaGPs6hcViwcXFBREREZgwYQLi4+PR1tYGFouF+vp65ObmoqamBlKp1Kiva0o6Ojpw7do1DB8+XKfAAwA2Njbw9/dHYmIipk6diqioKHr78fz58yguLkZzc7PWNTN9IYEnJCTEoMBz6tQpLFmyBDt27MCDDz5ovAXqyfDhw7FlyxZkZ2fj2rVruPvuu5Geno7CwkJzL+2OxHLMpBjMDovFQmRkJNatW4eXX34ZVVVV9EyidevWYfTo0UhPT0d6errRZxK1traisLAQ4eHhCAsLg0gkAo/HQ11dHYqLi+Hu7k5nAZbqN9fe3o6cnBzaPcIQVCfTqkq48/PzQVGUmvO0MethJGsLDg426D2cO3cODz/8MD777DM8/PDDFpHBpqWlqf29adMmbN++HZcvX8aoUaPMtKo7F7MFH2Jdz+Px1G7n8Xh9OuMOGzZMp8cz6A+LxUJISAheeOEFrFmzBnV1dcjMzERmZibWr1+PxMREehREeHi4QScX4oocFRVFq6kcHBzoLR/iN8fn81FaWmpUjzVjQRRhhtZHNMFms+Hl5QUvLy/ExMTQEu6SkhJ6RpOPjw98fHwMMiclgYcM49OXixcv4qGHHsKHH36IZcuWWUTg6YlCocDevXshFAqHZJPr3wGzCw7GjBmDzz77DEC34CA4OBjPPvtsn4KDrq4u/Pzzz/RtEyZMQEJCAiM4GCQoigKPx6NnEmVlZWHkyJF0IFJVdWkDuZqPjY3VyhVZKpXSgahngd5cdjuk+TIiIgLBwcGD9rqaRmV7eXnRWZEuozGEQiGuXbuGwMBAREZG6r2mP/74AxkZGXjnnXfwzDPPWFzgyc/Px/jx4yEWi+Hs7Izdu3djzpw5Jn1NhUJBZ6dKpbLXsElL+4wGC7NLrZcuXYr/+7//w5gxY/Dxxx/jp59+QnFxMfz8/LBkyRIEBgZi8+bNALqvqO666y5s2bIFc+fOxZ49e/Duu+8yUmszQVEUmpub1WYSRUZG0qMgYmNj+1WqkS01fS1/iN8cn89HU1MTHBwc4OvrCz8/v0HzmyMjBfTxyzM2miTcZDRGfxJu1cBjyGTdnJwcpKWlYf369VizZo1FnlSlUimqqqrQ1taGffv24euvv8bZs2cRGxtrktcjgYeiKKxduxbl5eXw9fXF4sWLMWnSJPo+S/ysTI3ZHQ4+//xzvP/++2hoaACHw8Gnn36KsWPHAuj2TwoNDcWuXbvox+/duxevv/46KioqEBUVhffee8/kVy4MA0M6+slMopMnT2L48OF0IEpMTFQLRGVlZaisrASHw4Gnp6fBr0/85ohSzNbWlg5EplKKke1CbSeoDiZisZgOzKqO5D3l90QS7u/vr7NAQpXr169j7ty5eOmll7Bu3bohczKdPn06IiIi8H//939GP7ZqUBkzZgzYbDbmzZuH3377DWKxGMuXL8eKFStgY2NzRwYgswcfhr8nHR0dOHr0KPbv34/jx4/D29sb8+fPR3p6OjIzM3Ht2jUcOHAAbm5uRn/tnmafqsV7Dw8Po/zIydhoQ4aoDRZSqZQOzCRDJOMPiouL4e/vj6ioKL0/l6KiIsyePRvPPvss3njjjSF1Er377rsRHBysdoFrbFasWIGqqir89ttvAIDHHnsMP/zwA0aOHIkVK1Zg5cqVsLW1veMCEKN2YzAJLi4uWLRoERYtWgShUEjPJJo1axYUCgUyMjJQUFCAcePGGd29oKdSrLm5GXw+H9evXweLxYKPjw/8/Pz09psjoykMGRs9mNja2iIgIAABAQGQy+VoampCXV0dKioqYGVlRavp9AnMJSUlmDdvHp544gmLDzyvvvoqZs+ejeDgYHR0dGD37t3IysrCiRMnjPo6qjUeoVAIf39/usdp1apVOHv2LM6dO4dXX30VH374IcRiMVatWmUx4pnBYui1jpsQXXzmdu7cicmTJ8PDwwMeHh6YPn36gL50dypOTk7IyMiAs7Mz/P398eWXX8LFxQULFy7EiBEj8PzzzyMrKwsymczor81ms+Ht7Y3Y2FhMmTKFHmVQUFCAs2fPoqCggLb/1wYej4f8/HzExcUNicDTE2tra7i6uqKzsxNBQUGIj4+HUqlEfn4+zp49q5P/3q1btzBv3jz84x//wNtvv23RgQfovmhYsmQJoqOjcc899+Dq1as4ceIE7r33XqO9RmtrKx149u7dCycnJyxfvhx33303fv75Z1y4cAH/+c9/kJqaimXLlqGpqQnff/89CgoKjLaGoQKz7fYnuvrMPfLII5g4cSImTJgAe3t7bN26FQcOHEBhYaHF7f9bAl9//TU+/PBD/Prrr3RhXiqV4vTp0/RMIgD0TKK77rpLJ7WWrpAaFY/HA5/Ph0wmU7P50ZSN1dfX48aNG4iPj4ePj4/J1mZKRCIRrl271stvrqf/Hvk8fH19adsjVSoqKjBr1ixkZGTg448/HpIWSMZm06ZNKC4uxmeffYb09HSIxWJcunSJ/mw+/PBD7N+/HydOnICLiwu+/vpr3L59G1OmTMGsWbPMvPrBhwk+f6Krz1xPFAoFPDw88Pnnn2PJkiWmXu6QQ6FQoL29vc95QnK5HOfOnaNnEonFYsybNw/p6em4++67TdpYSlEUOjo61MYfqJ54bWxsaGVeYmIivLy8TLYWUyIWi3Ht2jW6X6ivTEX18+Dz+RCJRPD09ER9fT2SkpIgl8sxc+ZMzJo1C19++SUTeP7kzJkzuOeeexAUFARnZ2dcuXIFzs7O9DbcBx98gN27d2P16tUICAjA0qVLsXnzZixdutTcSzcLTPCBfj5zPeno6ICvry/27t2r5trLoDsKhQK///479u3bh4MHD6KtrY2+yr733ntNujdOURSEQiGdEQmFQjg6OqKrqwsJCQkGT4E1FyTweHp6YuTIkTptkQmFQvD5fKxatQoXL16EtbU1OBwOfvzxR4Ocrv9OkAAzadIkXLx4EQ888AC++OILtQy5sbERDz/8MMrKytDV1YWFCxfe0ZNQmeCD7n6TwMBAXLx4Ua3b+eWXX8bZs2dx5cqVAY9B5pMUFhZarP3LUESpVOLKlSv0cDw+n48ZM2YgIyMDM2fOhIuLi0lfv6ysDBUVFbC3t4dIJIKHhwctZrDUiao9EYvFyM7OhoeHh86BRxUej4d77rkHHh4ecHFxwYULF5CSkoJXXnnljnWrJgo10jy6a9cu+Pr64v7778f8+fOxdetWhIaG0sGJBPLW1lYkJSWZe/lmhVG7GYEtW7Zgz549yMrKYgKPkWGz2Rg/fjzGjx+P999/Hzk5Odi3bx/eeecdPPnkk5g+fToyMjIwZ84co/fzVFZWoqqqCikpKXB3d4dIJAKfz0dDQwNKSkoseg4PQSKRIDs7G+7u7gYFHoFAgLS0NIwePRr/+9//YG1tDYFAgJ9//tkkcvmhgKqqjcfjwdnZGQsWLICbmxtOnz6N6dOnQy6XY9u2bQgJCUFTUxN27dqFF1980cwrtwyYzAeGbbt98MEHeOedd/Dbb78hNTV1EFbLAHRnRKoziW7evEm7FBtjJlF5eTkqKiqQnJys8eRK5vCQJk4XFxe1OTyWAAk8ZC6Svp9Hc3Mz5syZg4iICPz0009DaqKsqVC1yVm3bh0uXbqE1tZWeHl5YcuWLRg7dizy8vJw1113YezYsViwYAG2bduG+Ph47N+/38yrtwyY4PMnuvrMAcB7772HTZs24cSJExg3btxgLpdBBYqiUFxcTAeigoIC3HXXXfRMIh8fH51OvGVlZaiurkZKSopW23pSqVTN5sfJyYl2VzDXQDipVIpr164ZHHhaW1uRlpYGf39/ZGZmmlSBqA2bN29GZmYmiouL4eDggAkTJmDr1q2Ijo42y3qeffZZHDp0CDt27ICTkxNWrlwJiUSCa9euwdvbGyUlJViyZAns7e0RFRWFr7/+2izrtESY4PMnuvrMbd26FW+88QZ2796NiRMn0sdxdnY2m8ElQ3cgKisrowNRbm4uJkyYgPT0dMyfPx/+/v79qrzKyspQW1uLlJQUvf4d+xoI5+fnBxcXl0EJRCTwuLi4IC4uTu/XbG9vR0ZGBtzc3HDo0CGL2FKeNWsWFi1ahNGjR0Mul+O1115DQUEBioqKBj3jLCsrw+LFi/H5559jzJgx+Pbbb/Hyyy9jx44duO+++9DV1QVHR0d0dnaiq6tryIpVTAUTfFTQxWcuNDQUlZWVvY6xYcMGbNy4cRBXzdAXFEWhsrIS+/fvx4EDB3D58mWMGTOGnkkUFBREn5iVSiVKSkrA5/ORmppqlBOZQqFAY2MjeDweGhsbYWNjQwciNzc3kwQiqVSK7OxsODk5IS4uTm8ZdGdnJ+677z7Y2tri6NGjFlvTEggE8PX1xdmzZzFlypRBfe3c3Fzce++9qK6uxsGDB/Hkk0/im2++wYMPPoiWlhZ8+eWXWLZsGdP31wdM8GG4I6AoCrW1tfRMot9//x0cDgcZGRlIS0vD5s2bIZFIsGPHDpNIuRUKBW3zw+fz1SyA3N3djdIrQwKPo6Mj7eSgD11dXXjggQdAURSOHj1q0Zn8rVu3EBUVRbtOmApV3zXyvxsbG7FixQrExMTgq6++wo4dO7Bo0SIAwLVr17Bx40a89tprmDBhgsnWNZRhgg/DHQeZSXTgwAHs378fp0+fhpWVFVauXImVK1dixIgRJt0eI15qPB4PAoEAFEXRgcjT01OvoCGTyZCdnQ0HBweDAo9YLMbChQtpPz5XV1e9jjMYKJVKzJ8/H62trbhw4YLJXkdV1SaVSqFUKmFvbw+lUol//OMf2LNnD9atW0dvyTc1NWH+/PkICgrCnj17TLauoQ4TfCyYL774gt4GTExMxGeffYYxY8YM+Lw9e/Zg8eLFSE9Pp21rGHqjUCjw+OOPIysrC6tWrUJWVhZOnTqFqKgozJ8/HwsWLMDIkSNN2sFPbG1IU6tCoaCHwXl5eWllukoCj729PRISEvRer0QiwSOPPILGxkacPHkS7u7ueh1nsFi1ahWOHTuGCxcumGSWEpfLBYfDof/+7LPPcOTIEcjlcixatAgrV64EAEybNg3V1dUYN24cPD09cfnyZdja2po0IP4dYHwxLJQff/wRL7zwAjZs2ICcnBwkJiZi5syZ4PP5/T6voqICa9euxeTJkwdppUOXDz/8EJcuXcKFCxfw8ssv4+jRo+DxeHj55ZdRWFiIKVOmICUlBRs2bACXy9XKbFNXWCwWPDw8EBMTg8mTJyM5ORm2trYoLS3F2bNncf36dTQ0NEAul2t8vkwmQ05ODuzs7AwKPFKpFEuXLkV9fT2OHz9u8YHn2WefxZEjR3DmzBmTBJ5DV6WmhwAAEnJJREFUhw4hOTkZP/zwAwBgx44dWL9+PeLi4hAYGIgnn3wSa9euBdBtq7NkyRK6xpeens4EHi1gMh8LRR+vOYVCgSlTpmDFihU4f/48WltbmcynHzo7OyEUCuHn56fx/vb2drWZRL6+vnRGlJKSYvKMqLOzk86IRCIRvLy84OvrCx8fH9jY2EAulyMnJwc2Nja9hvXpgkwmw2OPPYaSkhKcPn3aok1TKYrCc889hwMHDiArKwtRUVEmeZ3W1lZs3boVH374IXbt2oWOjg54eXnhgQcegEKhwI8//kjP4iHtGQy6wTgcWCCkcPzqq6/St7HZbEyfPh2XLl3q83lvvfUWfH198dhjj+H8+fODsdQhzUCyeFdXVyxevBiLFy+GUCjEsWPHkJmZifnz58PNzQ3z589HRkYGxo4da/SZRCwWCy4uLnBxcUFkZCQ6OzvB5/NRVVWFoqIieHh4QCQSGbzVJpfL8dRTT6GoqAhnzpyx6MADAM888wx2796NQ4cOwcXFBQ0NDQAANzc3gxV5qqICd3d3bN68GVZWVnj00Ufh6+uLTz/9FED3vKiHH34YNjY2tCkoE4B0h9l2s0AaGxuhUCh6XZH7+fnRP7aeXLhwAd988w127tw5GEu843BycsIDDzyA3bt3o6GhAZ999hk6Ojrw0EMPITo6GmvWrMHZs2f73B4zFGdnZ4SHh2PcuHEYO3Ysurq6IJPJ0NraitzcXFRVVUEsFut0TIVCgeeeew7Z2dn47bff+swALYnt27ejra0NU6dOhb+/P/3fjz/+aPCxWSwWKisrcfr0aQDAl19+CZFIhK1bt6KpqQlFRUVqj3/wwQexZ88efPHFF7TYgEF7mMznb0BHRwceffRR7Ny5E97e3uZezt8eBwcHuldIKpXit99+Q2ZmJpYsWQIWi4W5c+diwYIFmDJlitEdAeRyOYqLi+Ho6AgOhwOZTEaPgigtLYWrqyvdS9RfJqBUKrFmzRpcuHABZ86cQUBAgFHXaSpMVSWgKApdXV144oknYGNjg+PHj+ODDz7AgQMHMGvWLCiVSrzyyitwd3fH6tWr6efNnz8f586dY6y19ICp+VggunrNcblcJCUlqW39kOI4m81GSUkJIiIiBmXtdzIymYyeSXTo0CFIJBLMnTsXGRkZmDZtmsEOAQqFArm5uWCxWOBwOL22+iQSCQQCAXg8HlpaWuDs7Aw/P79efnNKpZIWWGRlZSEsLMygdf2dyMvLwyOPPIKioiK8+uqr2LRpE4DusRJfffUVXnrpJbz33nu02IBBf5jgY6Ho4jUnFotx69Yttdtef/11dHR04JNPPsGIESPM7sl1p6FQKHDhwgV6JlF7eztmz56NjIwMTJ8+XedGVhJ4APS60NCETCajA1FTUxNYLBaOHTuG+++/H4cOHUJmZibOnDljsoL9UEUoFGLq1Kno7OxEdHQ0VqxYgfnz59P3ff3111i3bh3WrFnDbLUZCBN8LBRdveZ6smzZMkbtZiEolUpcvnyZDkQCgUBtJtFADgIKhYKWeicnJ+ssbpDL5cjPz8f69etx7tw5AMDy5cvxxBNPIDU11SzGp5ZMZ2cnKisr8eyzz8Le3h5PPPEEPa+Ioihs2bIF33//PXJyckw62PDvDiM4sFAWLlyIDz74AG+88QY4HA64XC6OHz9OF4WrqqpQX19v5lUyaAObzcaECROwbds23Lp1C6dPn0ZUVBTefvtthIaGYtGiRfjhhx/Q1tbWq6ahUCiQl5cHpVKpVcajCTJ5dMKECfDw8MAHH3wAkUiE6dOnIzQ0FIWFhcZ6q38LnJ2dMWrUKGzbtg1SqRQ7d+7ETz/9BAB47rnnUFVVxQQeI8BkPgwMZkKpVOL69evYv38/MjMzcevWLdxzzz2YP38+5s2bB1tbWzzxxBN45JFHMHPmTFhb66cPoigK27Ztw8cff4zTp08jMTERQHeN6NSpU5g2bZrFGoeam4KCArzyyiuorKyEra0tKisrcfHiRYwYMcLcSxvyMMGHgcECoCgKN27coEdBFBYWwtnZGQ4ODjh27BgiIyP12h6jKAqfffYZ3nvvPZw8eZJRZelBeXk5Tp06hfr6eixZsgQhISHmXtLfA4qBQUs+//xzKiQkhLKzs6PGjBlDXblypd/Ht7S0UE8//TQ1bNgwytbWloqKiqKOHj06SKsduojFYuruu++mAgMDKQ6HQ1lbW1NTpkyhtm3bRt26dYvq7OykhELhgP91dnZSH374IeXm5kZdunTJ3G+LoiiKOnv2LDVv3jzK39+fAkAdOHDA3EtiMBNMzYdBK3T1mpNKpbj33ntRUVGBffv2oaSkBDt37mRmmwyAQqHAwoUL0dbWhoKCAuTk5KC0tBRpaWnYt28foqOjMWPGDHz++eeorq7us++Foih899132LhxI37++WeLmbQrFAqRmJiIL774wtxLYTA35o5+DEODMWPGUM888wz9t0KhoAICAqjNmzdrfPz27dup8PBwSiqVDtYS/zZ8/fXXVFNTU6/blUolVVVVRX388cfUlClTKCsrK2r06NHUpk2bqIKCAjoj6uzspLZv3045OztTZ86cGfw3oCVgMp87GqbmwzAguja9AsCcOXPg6ekJR0dHHDp0CD4+Pnj44Yexbt06o/ug3YlQFIWGhgYcOHAAmZmZOHv2LOLi4pCeng47Ozts2rQJmZmZmDFjhrmX2icsFgsHDhxQ+04x3Dkw9joMA9Kf11xxcbHG59y+fRunT5/GI488gl9++QW3bt3C008/DZlMhg0bNgzGsv/WsFgs+Pv74+mnn8aqVavQ1NSEQ4cOYffu3Th9+jT++9//WnTgYWBggg+DSVAqlfD19cWOHTtgZWWFlJQU1NbW4v3332eCj5FhsVjw9vbGY489hhUrVqC2ttYkM24YGIwJE3wYBsTb2xtWVlbg8Xhqt/N4PAwbNkzjc/z9/WFjY6O2xTZy5Eg0NDRAKpUydj8mgsViMYGHYUjAqN0YBsTW1hYpKSk4deoUfZtSqcSpU6cwfvx4jc+ZOHEibt26pTb9s7S0FP7+/kzgYWBgYIIPg3a88MIL2LlzJ77//nvcuHEDq1atglAoxPLlywEAS5YsURt+t2rVKjQ3N2P16tUoLS3F0aNH8e677+KZZ54x11tgsAA6OzvB5XLB5XIBdDdwcrlcVFVVmXdhDIMOs+1mwRAhoiUYPy5cuBACgQBvvPEGGhoawOFwennNqU7TDAoKwokTJ7BmzRokJCQgMDAQq1evxrp168z1FhgsgGvXrmHatGn03y+88AKAbuXkrl27zLQqBnPASK0tFJFIpOa3ZUmBiIGBgcFQmOBjoSxYsAApKSmYPXs2AgIC4O/vr3a/UqkEm83GjRs38O9//xsjR47EokWLmHoKAwPDkICp+Vgg9fX1uHXrFnbu3IkPPvgAHA6HHtlMIBnQ+fPn8f3332PZsmV4+OGH0djYaK5lm4UvvvgCoaGhsLe3x9ixY/HHH3/0+/iPP/4Y0dHRcHBwQFBQENasWQOxWDxIq2VgYCAwNR8LhDjoZmRkYO3atfjoo49QWFgIW1tbUBQFFotFB5+cnByMHj0ae/bsAYvFgo2NjZlXP3gQv7mvvvoKY8eOxccff4yZM2eipKQEvr6+vR6/e/duvPLKK/j2228xYcIElJaWYtmyZWCxWNi2bZsZ3gEDw50Ls+1mgSxZsgT19fX49ttvERQURG+xEUgAunHjBp577jkkJCT0efIkj/07MnbsWIwePRqff/45gO6tyKCgIDz33HO9Ro0DwLPPPosbN26oScZffPFFXLlyBRcuXBi0dTMwMDDbbhZHXV0dSkpKMG7cOAQFBQGAWuAB/hIfXL58GZ2dnbjrrrsAdDsiA4BAIKAfSwKPar/N3wGpVIrs7GxMnz6dvo3NZmP69Om4dOmSxudMmDAB2dnZ9Nbc7du38csvv2DOnDmDsmYGBoa/YLbdLIwzZ86AoiikpKQA0Jy5kGB09epVuLq6YuLEiQD+CjRTpkzBfffdh5kzZ8LGxgbjx49XC2AKhQIsFqtXUBtK6OM3R2pikyZNAkVRkMvleOqpp/Daa68NxpIZGBhUGLpnn78pmZmZ8PHxAYfD0Xg/yXpKS0tx69YtxMbGwtvbGxRFgc1mo6qqCtXV1fjpp5/w3//+F/fddx8SEhJQWVlJH8PKyqpX4Kmrq8MzzzyDF198EbW1tSZ7f+YkKysL7777Lr788kvk5OQgMzMTR48exdtvv23upQ05dBV6MDD0hAk+FoRUKkV0dDSSk5MRGhoKoHdfj+qWW3t7O6ZMmQLgr221w4cPg81m4/XXX8f27dtx+fJlSKVS7N69G5mZmZg9ezYWLlxId5gTPD09sWjRInzyySdIS0vDjRs3TPtmDUQfv7n169fj0UcfxeOPP474+HgsWLAA7777LjZv3vy325Y0JboOFmRg0AQTfCwIW1tbvPvuu/1eiatuuTk7O/facvvhhx9w//33Y8mSJbCysoK7uzsiIiLw6aefIisrC2vXroVIJMLq1ashkUjo49rb22Py5MmYPHkyxo0b1+cJ3FLQx2+uq6urV8ZHjE8Z3Y32bNu2DStXrsTy5csRGxuLr776Co6Ojvj222/NvTSGIQQTfCwIiqL6vQInJ8iysjKUlpYiJiaGrnmw2WzU1NTgjz/+wMKFC+lgJBQKkZeXh2eeeQaffPIJ7rnnHqxYsQJVVVU4e/YsgL+ypuLiYpSWlmLs2LHw8PAw5Vs1Crr6zaWlpWH79u3Ys2cPysvL8euvv2L9+vVIS0tjBtxpiT5CDwYGTTCCAwtCtX9HE0R88Mcff6C9vR0TJkwA0C0gsLKywi+//AIfHx+MGTOGfs7169dRX1+PFStW0Md2cXEBi8WCs7MzAEAul8PW1hYHDhyAn58f4uLiTPgujYeufnOvv/46WCwWXn/9ddTW1sLHxwdpaWnYtGmTud7CkEMfoQcDgyaY4DOEICfSs2fPwtbWFg8//DCAv7bcPvvsM0yZMgWenp4AuoPK4cOHkZCQgICAAACATCZDTk4ORCIRHbxIY+rRo0eRkpKCsLCwQX1fhvDss8/i2Wef1XhfVlaW2t/W1tbYsGEDM8yOgcECYLbdhhgdHR2wt7fH+fPnMXfuXNTU1IDNZkMul2PWrFl4/PHH6cc2Njbi+PHjePTRR+nbBAIBTp06RfcGSaVSsFgslJeXo6KiAuPHj6eDFwNDT/QRejAwaIIJPkMMFxcXfPjhh8jJycHChQvpWoW1tTXef/99tb34W7duoaKiAhkZGfRt5eXlyMvLwyOPPALgrzpSZmYmvLy8EB8fP3hvhmHIoY/Qg4FBE0zwGYJYWVmBw+FgyZIltNu1UqnsJVaYNGkSbt26hfDwcADd23CnT59Ga2sr0tLSAPy15Xb48GGkpKTQj2XQj3PnziEtLQ0BAQFgsVg4ePDggM/JyspCcnIy7OzsEBkZafFzbQYSejAwaAMTfP4msNlsjY4FqsGEzWYjMjISTzzxBIDuLTc2m43q6mqUlZVh/Pjx8PLyGrQ1/x0RCoVITEzEF198odXjy8vLMXfuXEybNg1cLhfPP/88Hn/8cZw4ccLEK9WfhQsX4oMPPsAbb7wBDocDLperJvRgYNAGxliUAZ988gm+/vpr7Ny5E+PGjTP3cv42sFgsHDhwQG3bsyfr1q3D0aNHUVBQQN+2aNEitLa24vjx44OwSgYG88BkPncYcrmc/t+XL19Gc3Mzfv31V6SmpiIiIsKMK7szuXTpklqdDgBmzpzJ9Mww/O1hgs8dhrV1t7peKpXi0qVL8Pf3xy+//IKEhAT4+PiYeXV3Hg0NDRp7Ztrb2yESicy0KgYG08P0+dyh2NraYs2aNVi4cCGKiooQEhJi7iUxMDDcQTDB5w4nICCAbkBlGHyGDRumsWfG1dUVDg4OZloVA4PpYbbdGBjMyPjx49V6ZgDg119/ZXpmGP72MMGHgcGIdHZ2gsvl0iMrysvLweVyUVVVBQB49dVXsWTJEvrxTz31FG7fvo2XX34ZxcXF+PLLL/HTTz9hzZo15lg+A8OgwUitGRiMSFZWFqZNm9br9qVLl2LXrl1YtmwZKioq1HznsrKysGbNGhQVFWH48OFYv349li1bNniLZmAwA0zwYWBgYGAYdJhtNwYGBgaGQYcJPgwMDAwMgw4TfBgYGBgYBh0m+DAwMDAwDDpM8GFgYGBgGHSY4MPAwMDAMOgwwYeBgYGBYdBhgg8DAwMDw6DDBB8GBgYGhkGHCT4MDAwMDIMOE3wYGBgYGAad/wfhUwqWnbE4XgAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "trainer.saveplot(issave=True, isplot=True)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "pinnx", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.11" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/docs/experimental_docs/unit-examples-forward/Laplace_disk.py b/docs/experimental_docs/unit-examples-forward/Laplace_disk.py new file mode 100644 index 000000000..73acafb9e --- /dev/null +++ b/docs/experimental_docs/unit-examples-forward/Laplace_disk.py @@ -0,0 +1,64 @@ +import brainstate as bst +import brainunit as u +import numpy as np + +import deepxde.experimental as deepxde + +# geom = experimental.geometry.Rectangle(xmin=[0, 0], xmax=[1, 2 * np.pi]) +# geom = geom.to_dict_point("r", "theta") + +geom = deepxde.geometry.Rectangle( + xmin=[0, 0], + xmax=[1, 2 * np.pi], +).to_dict_point(r=u.meter, theta=u.radian) + +uy = u.volt / u.meter +bc = deepxde.icbc.DirichletBC( + lambda x: {'y': u.math.cos(x['theta']) * uy}, + lambda x, on_boundary: u.math.logical_and(on_boundary, u.math.allclose(x['r'], 1 * u.meter)), +) + + +def solution(x): + r, theta = x['r'], x['theta'] + # TODO: Why add more divide u.meter? + return {'y': r * u.math.cos(theta) * uy / u.meter} + + +def pde(x, y): + jacobian = net.jacobian(x) + hessian = net.hessian(x) + + dy_r = jacobian["y"]["r"] + dy_rr = hessian["y"]["r"]["r"] + dy_thetatheta = hessian["y"]["theta"]["theta"] + return x['r'] * dy_r + x['r'] ** 2 * dy_rr + dy_thetatheta + + +# Use [r*sin(theta), r*cos(theta)] as features, +# so that the network is automatically periodic along the theta coordinate. +def feature_transform(x): + x = deepxde.utils.array_to_dict(x, ["r", "theta"], keep_dim=True) + return u.math.concatenate([x['r'] * u.math.sin(x['theta']), + x['r'] * u.math.cos(x['theta'])], axis=-1) + + +net = deepxde.nn.Model( + deepxde.nn.DictToArray(r=u.meter, theta=u.radian), + deepxde.nn.FNN([2] + [20] * 3 + [1], "tanh", input_transform=feature_transform), + deepxde.nn.ArrayToDict(y=uy), +) + +problem = deepxde.problem.PDE( + geom, + pde, + bc, + net, + num_domain=2540, + num_boundary=80, + solution=solution +) + +trainer = deepxde.Trainer(problem) +trainer.compile(bst.optim.Adam(1e-3), metrics=["l2 relative error"]).train(iterations=15000) +trainer.saveplot(issave=True, isplot=True) diff --git a/docs/experimental_docs/unit-examples-forward/burgers.ipynb b/docs/experimental_docs/unit-examples-forward/burgers.ipynb new file mode 100644 index 000000000..d50c1c462 --- /dev/null +++ b/docs/experimental_docs/unit-examples-forward/burgers.ipynb @@ -0,0 +1,637 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "e0159dcbb63a3365", + "metadata": {}, + "source": [ + "# Burgers equation\n", + "\n", + "\n", + "## Problem setup\n", + "\n", + "\n", + "We will solve a Burgers equation:\n", + "\n", + "$$\n", + "\\frac{\\partial u}{\\partial t} + u\\frac{\\partial u}{\\partial x} = \\nu\\frac{\\partial^2u}{\\partial x^2}, \\qquad x \\in [-1, 1], \\quad t \\in [0, 1]\n", + "$$\n", + "\n", + "\n", + "with the Dirichlet boundary conditions and initial conditions\n", + "\n", + "$$\n", + "u(-1,t)=u(1,t)=0, \\quad u(x,0) = - \\sin(\\pi x).\n", + "$$\n", + "\n", + "## Dimensional Analysis\n", + "\n", + "### Step 1: Assign Dimensions to Variables\n", + "\n", + "1. **Spatial Coordinate $x$:**\n", + " - The dimension of $x$ is length:\n", + "\n", + " $$\n", + " [x] = L.\n", + " $$\n", + "\n", + "2. **Time $t$:**\n", + " - The dimension of time is:\n", + "\n", + " $$\n", + " [t] = T.\n", + " $$\n", + "\n", + "3. **Velocity $u$:**\n", + " - Velocity has dimensions of length per unit time:\n", + "\n", + " $$\n", + " [u] = L / T.\n", + " $$\n", + "\n", + "4. **Viscosity $\\nu$:**\n", + " - The term $\\nu \\frac{\\partial^2 u}{\\partial x^2}$ involves the second spatial derivative of velocity, which must have the same dimensions as the time derivative $\\frac{\\partial u}{\\partial t}$.\n", + "\n", + "---\n", + "\n", + "### Step 2: Analyze the Dimensions of Each Term\n", + "\n", + "1. **Time Derivative Term:**\n", + " - The time derivative $\\frac{\\partial u}{\\partial t}$ has dimensions:\n", + "\n", + " $$\n", + " \\left[\\frac{\\partial u}{\\partial t}\\right] = \\frac{[u]}{[t]} = \\frac{L / T}{T} = \\frac{L}{T^2}.\n", + " $$\n", + "\n", + "2. **Advection Term:**\n", + " - The advection term $u \\frac{\\partial u}{\\partial x}$ involves the spatial derivative of velocity:\n", + "\n", + " $$\n", + " \\left[u \\frac{\\partial u}{\\partial x}\\right] = [u] \\cdot \\frac{[u]}{[x]} = \\frac{L}{T} \\cdot \\frac{L / T}{L} = \\frac{L}{T^2}.\n", + " $$\n", + "\n", + "3. **Diffusion Term:**\n", + " - The diffusion term $\\nu \\frac{\\partial^2 u}{\\partial x^2}$ involves the second spatial derivative of velocity:\n", + "\n", + " $$\n", + " \\left[\\frac{\\partial^2 u}{\\partial x^2}\\right] = \\frac{[u]}{[x]^2} = \\frac{L / T}{L^2} = \\frac{1}{L T}.\n", + " \n", + " $$\n", + " - Therefore, the diffusion term has dimensions:\n", + "\n", + " $$\n", + " \\left[\\nu \\frac{\\partial^2 u}{\\partial x^2}\\right] = [\\nu] \\cdot \\frac{1}{L T} = \\frac{L}{T^2}.\n", + " $$\n", + "\n", + "---\n", + "\n", + "### Step 3: Determine the Dimensions of $\\nu$\n", + "\n", + "- The diffusion term $\\nu \\frac{\\partial^2 u}{\\partial x^2}$ must have the same dimensions as the time derivative $\\frac{\\partial u}{\\partial t}$:\n", + "\n", + " $$\n", + " [\\nu] \\cdot \\frac{1}{L T} = \\frac{L}{T^2} \\implies [\\nu] = \\frac{L^2}{T}.\n", + " $$\n", + "- Therefore, the viscosity $\\nu$ has dimensions of kinematic viscosity:\n", + "\n", + " $$\n", + " [\\nu] = \\frac{L^2}{T}.\n", + " $$\n", + "\n", + "---\n", + "\n", + "### Step 4: Summary of Dimensions\n", + "\n", + "| Variable/Parameter | Physical Meaning | Dimensions |\n", + "|------------------------|-----------------------------------|-----------------------|\n", + "| $x$ | Spatial coordinate | $L$ |\n", + "| $t$ | Time | $T$ |\n", + "| $u$ | Velocity | $L / T$ |\n", + "| $\\nu$ | Kinematic viscosity | $L^2 / T$ |\n", + "\n", + "---\n", + "\n", + "### Step 5: Initial and Boundary Conditions\n", + "\n", + "1. **Boundary Conditions:**\n", + " - The boundary conditions $u(-1,t) = u(1,t) = 0$ are given in meters per second:\n", + "\n", + " $$\n", + " [u(-1,t)] = [u(1,t)] = L / T.\n", + " $$\n", + "\n", + "2. **Initial Condition:**\n", + " - The initial condition $u(x,0) = -\\sin(\\pi x)$ is given in meters per second:\n", + " \n", + " $$\n", + " [u(x,0)] = L / T.\n", + " $$\n", + " - The term $\\sin(\\pi x)$ is dimensionless because $x$ is in meters, and $\\pi$ is a dimensionless constant." + ] + }, + { + "cell_type": "markdown", + "id": "5f173a598aa4fb4", + "metadata": {}, + "source": [ + "## Implementation" + ] + }, + { + "cell_type": "markdown", + "id": "a491f73861dcaa4", + "metadata": {}, + "source": [ + "This description goes through the implementation of a solver for the above described Burgers equation step-by-step.\n", + "\n", + "First, import the libraries we need:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "a6e9a11ec74e35dd", + "metadata": { + "ExecuteTime": { + "end_time": "2024-11-26T08:31:14.883767Z", + "start_time": "2024-11-26T08:31:12.197302Z" + } + }, + "outputs": [], + "source": [ + "import brainstate as bst\n", + "import brainunit as u\n", + "import numpy as np\n", + "import deepxde.experimental as deepxde" + ] + }, + { + "cell_type": "markdown", + "id": "95245422ff39b28d", + "metadata": {}, + "source": [ + "We begin by defining a computational geometry and time domain. We can use a built-in class ``Interval`` and ``TimeDomain`` and we combine both the domains using ``GeometryXTime`` as follows:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "2b87ed2d174e56cf", + "metadata": { + "ExecuteTime": { + "end_time": "2024-11-26T08:31:14.937721Z", + "start_time": "2024-11-26T08:31:14.888260Z" + } + }, + "outputs": [], + "source": [ + "geometry = deepxde.geometry.GeometryXTime(\n", + " geometry=deepxde.geometry.Interval(-1., 1.),\n", + " timedomain=deepxde.geometry.TimeDomain(0., 0.99)\n", + ").to_dict_point(x=u.meter, t=u.second)" + ] + }, + { + "cell_type": "markdown", + "id": "271c9ad81e74bf98", + "metadata": {}, + "source": [ + "Next, we express the PDE residual of the Burgers equation:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "89d86ee9fcaa2e22", + "metadata": { + "ExecuteTime": { + "end_time": "2024-11-26T08:31:15.009040Z", + "start_time": "2024-11-26T08:31:14.993264Z" + } + }, + "outputs": [], + "source": [ + "v = 0.01 / u.math.pi * u.meter ** 2 / u.second\n", + "\n", + "\n", + "def pde(x, y):\n", + " jacobian = approximator.jacobian(x)\n", + " hessian = approximator.hessian(x)\n", + " dy_x = jacobian['y']['x']\n", + " dy_t = jacobian['y']['t']\n", + " dy_xx = hessian['y']['x']['x']\n", + " residual = dy_t + y['y'] * dy_x - v * dy_xx\n", + " return residual" + ] + }, + { + "cell_type": "markdown", + "id": "5d8df2efba443bb4", + "metadata": {}, + "source": [ + "Next, we consider the boundary/initial condition. ``on_boundary`` is chosen here to use the whole boundary of the computational domain in considered as the boundary condition. We include the ``geomtime`` space, time geometry created above and ``on_boundary`` as the BCs in the ``DirichletBC`` function of DeepXDE. We also define ``IC`` which is the inital condition for the burgers equation and we use the computational domain, initial function, and ``on_initial`` to specify the IC.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "ce3ebafdc08158a0", + "metadata": { + "ExecuteTime": { + "end_time": "2024-11-26T08:31:15.018480Z", + "start_time": "2024-11-26T08:31:15.015094Z" + } + }, + "outputs": [], + "source": [ + "uy = u.meter / u.second\n", + "\n", + "bc = deepxde.icbc.DirichletBC(lambda x: {'y': 0. * uy})\n", + "ic = deepxde.icbc.IC(lambda x: {'y': -u.math.sin(u.math.pi * x['x'] / u.meter) * uy})" + ] + }, + { + "cell_type": "markdown", + "id": "a0d5bb9643b9573b", + "metadata": {}, + "source": [ + "Next, we choose the network. Here, we use a fully connected neural network of depth 4 (i.e., 3 hidden layers) and width 20:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "6c6eefc678fcc466", + "metadata": { + "ExecuteTime": { + "end_time": "2024-11-26T08:31:15.418417Z", + "start_time": "2024-11-26T08:31:15.025837Z" + } + }, + "outputs": [], + "source": [ + "approximator = deepxde.nn.Model(\n", + " deepxde.nn.DictToArray(x=u.meter, t=u.second),\n", + " deepxde.nn.FNN(\n", + " [geometry.dim] + [20] * 3 + [1],\n", + " \"tanh\",\n", + " bst.init.KaimingUniform()\n", + " ),\n", + " deepxde.nn.ArrayToDict(y=uy)\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "48a114491365b25a", + "metadata": {}, + "source": [ + "Now, we have specified the geometry, PDE residual, and boundary/initial condition. We then define the ``TimePDE`` problem as\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "aa60a6f8cad0dace", + "metadata": { + "ExecuteTime": { + "end_time": "2024-11-26T08:31:16.586859Z", + "start_time": "2024-11-26T08:31:15.430286Z" + } + }, + "outputs": [], + "source": [ + "problem = deepxde.problem.TimePDE(\n", + " geometry,\n", + " pde,\n", + " [bc, ic],\n", + " approximator,\n", + " num_domain=2540,\n", + " num_boundary=80,\n", + " num_initial=160,\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "de04e3c7d5dce9cb", + "metadata": {}, + "source": [ + "The number 2540 is the number of training residual points sampled inside the domain, and the number 80 is the number of training points sampled on the boundary. We also include 160 initial residual points for the initial conditions.\n", + "\n", + "Now, we have the PDE problem and the network. We build a ``Trainer`` and choose the optimizer and learning rate:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "29fa25c853bbc6f6", + "metadata": { + "ExecuteTime": { + "end_time": "2024-11-26T08:33:20.343840Z", + "start_time": "2024-11-26T08:31:16.598749Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Compiling trainer...\n", + "'compile' took 0.047883 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric\n", + "0 [0.15803409 * 10.0^0 * ((meter / second) / second) ** 2, [0.15803409 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 0.25960198 * meter / second}}, {'ibc0': {'y': 0.25960198 * meter / second}}, \n", + " {'ibc1': {'y': 1.1659584 * meter / second}}] {'ibc1': {'y': 1.1659584 * meter / second}}] \n", + "1000 [0.04754296 * 10.0^0 * ((meter / second) / second) ** 2, [0.04754296 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 0.00308682 * meter / second}}, {'ibc0': {'y': 0.00308682 * meter / second}}, \n", + " {'ibc1': {'y': 0.06809452 * meter / second}}] {'ibc1': {'y': 0.06809452 * meter / second}}] \n", + "2000 [0.04182805 * 10.0^0 * ((meter / second) / second) ** 2, [0.04182805 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 0.00125541 * meter / second}}, {'ibc0': {'y': 0.00125541 * meter / second}}, \n", + " {'ibc1': {'y': 0.05376936 * meter / second}}] {'ibc1': {'y': 0.05376936 * meter / second}}] \n", + "3000 [0.03440975 * 10.0^0 * ((meter / second) / second) ** 2, [0.03440975 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 0.00054205 * meter / second}}, {'ibc0': {'y': 0.00054205 * meter / second}}, \n", + " {'ibc1': {'y': 0.04500021 * meter / second}}] {'ibc1': {'y': 0.04500021 * meter / second}}] \n", + "4000 [0.0215442 * 10.0^0 * ((meter / second) / second) ** 2, [0.0215442 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 0.00029352 * meter / second}}, {'ibc0': {'y': 0.00029352 * meter / second}}, \n", + " {'ibc1': {'y': 0.03042006 * meter / second}}] {'ibc1': {'y': 0.03042006 * meter / second}}] \n", + "5000 [0.01140877 * 10.0^0 * ((meter / second) / second) ** 2, [0.01140877 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 0.00016095 * meter / second}}, {'ibc0': {'y': 0.00016095 * meter / second}}, \n", + " {'ibc1': {'y': 0.02001206 * meter / second}}] {'ibc1': {'y': 0.02001206 * meter / second}}] \n", + "6000 [0.00863622 * 10.0^0 * ((meter / second) / second) ** 2, [0.00863622 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 9.4245006e-05 * meter / second}}, {'ibc0': {'y': 9.4245006e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.01318286 * meter / second}}] {'ibc1': {'y': 0.01318286 * meter / second}}] \n", + "7000 [0.00690631 * 10.0^0 * ((meter / second) / second) ** 2, [0.00690631 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 5.483637e-05 * meter / second}}, {'ibc0': {'y': 5.483637e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.00822749 * meter / second}}] {'ibc1': {'y': 0.00822749 * meter / second}}] \n", + "8000 [0.00483667 * 10.0^0 * ((meter / second) / second) ** 2, [0.00483667 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 2.3079416e-05 * meter / second}}, {'ibc0': {'y': 2.3079416e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.00571595 * meter / second}}] {'ibc1': {'y': 0.00571595 * meter / second}}] \n", + "9000 [0.00386771 * 10.0^0 * ((meter / second) / second) ** 2, [0.00386771 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.4185833e-05 * meter / second}}, {'ibc0': {'y': 1.4185833e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.00445467 * meter / second}}] {'ibc1': {'y': 0.00445467 * meter / second}}] \n", + "10000 [0.00332004 * 10.0^0 * ((meter / second) / second) ** 2, [0.00332004 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.3227182e-05 * meter / second}}, {'ibc0': {'y': 1.3227182e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.00389429 * meter / second}}] {'ibc1': {'y': 0.00389429 * meter / second}}] \n", + "11000 [0.00295054 * 10.0^0 * ((meter / second) / second) ** 2, [0.00295054 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.3391712e-05 * meter / second}}, {'ibc0': {'y': 1.3391712e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.00342724 * meter / second}}] {'ibc1': {'y': 0.00342724 * meter / second}}] \n", + "12000 [0.00252938 * 10.0^0 * ((meter / second) / second) ** 2, [0.00252938 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 1.0651251e-05 * meter / second}}, {'ibc0': {'y': 1.0651251e-05 * meter / second}}, \n", + " {'ibc1': {'y': 0.00329811 * meter / second}}] {'ibc1': {'y': 0.00329811 * meter / second}}] \n", + "13000 [0.00229796 * 10.0^0 * ((meter / second) / second) ** 2, [0.00229796 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 8.255725e-06 * meter / second}}, {'ibc0': {'y': 8.255725e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00314907 * meter / second}}] {'ibc1': {'y': 0.00314907 * meter / second}}] \n", + "14000 [0.00211558 * 10.0^0 * ((meter / second) / second) ** 2, [0.00211558 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 6.807138e-06 * meter / second}}, {'ibc0': {'y': 6.807138e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.002992 * meter / second}}] {'ibc1': {'y': 0.002992 * meter / second}}] \n", + "15000 [0.002326 * 10.0^0 * ((meter / second) / second) ** 2, [0.002326 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 7.791486e-06 * meter / second}}, {'ibc0': {'y': 7.791486e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00277965 * meter / second}}] {'ibc1': {'y': 0.00277965 * meter / second}}] \n", + "\n", + "Best trainer at step 15000:\n", + " train loss: 5.11e-03\n", + " test loss: 5.11e-03\n", + " test metric: []\n", + "\n", + "'train' took 123.689102 s\n", + "\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trainer = deepxde.Trainer(problem)\n", + "trainer.compile(bst.optim.Adam(1e-3)).train(iterations=15000)" + ] + }, + { + "cell_type": "markdown", + "id": "1cff205141601ec3", + "metadata": {}, + "source": [ + "After we train the network using Adam, we continue to train the network using L-BFGS to achieve a smaller loss:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "5013a7d8bcac6ee9", + "metadata": { + "ExecuteTime": { + "end_time": "2024-11-26T08:33:36.821381Z", + "start_time": "2024-11-26T08:33:20.374591Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Compiling trainer...\n", + "'compile' took 0.105205 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric\n", + "15000 [0.002326 * 10.0^0 * ((meter / second) / second) ** 2, [0.002326 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 7.791486e-06 * meter / second}}, {'ibc0': {'y': 7.791486e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00277965 * meter / second}}] {'ibc1': {'y': 0.00277965 * meter / second}}] \n", + "15200 [0.00468681 * 10.0^0 * ((meter / second) / second) ** 2, [0.00468681 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 6.556747e-06 * meter / second}}, {'ibc0': {'y': 6.556747e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00299743 * meter / second}}] {'ibc1': {'y': 0.00299743 * meter / second}}] \n", + "15400 [0.00374917 * 10.0^0 * ((meter / second) / second) ** 2, [0.00374917 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 5.420788e-06 * meter / second}}, {'ibc0': {'y': 5.420788e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00296684 * meter / second}}] {'ibc1': {'y': 0.00296684 * meter / second}}] \n", + "15600 [0.00311677 * 10.0^0 * ((meter / second) / second) ** 2, [0.00311677 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.825496e-06 * meter / second}}, {'ibc0': {'y': 4.825496e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00294279 * meter / second}}] {'ibc1': {'y': 0.00294279 * meter / second}}] \n", + "15800 [0.00269283 * 10.0^0 * ((meter / second) / second) ** 2, [0.00269283 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.55498e-06 * meter / second}}, {'ibc0': {'y': 4.55498e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00292296 * meter / second}}] {'ibc1': {'y': 0.00292296 * meter / second}}] \n", + "16000 [0.00241696 * 10.0^0 * ((meter / second) / second) ** 2, [0.00241696 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.4667136e-06 * meter / second}}, {'ibc0': {'y': 4.4667136e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00290674 * meter / second}}] {'ibc1': {'y': 0.00290674 * meter / second}}] \n", + "16200 [0.00223442 * 10.0^0 * ((meter / second) / second) ** 2, [0.00223442 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.4755107e-06 * meter / second}}, {'ibc0': {'y': 4.4755107e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00289299 * meter / second}}] {'ibc1': {'y': 0.00289299 * meter / second}}] \n", + "16400 [0.00212654 * 10.0^0 * ((meter / second) / second) ** 2, [0.00212654 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.4758385e-06 * meter / second}}, {'ibc0': {'y': 4.4758385e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00288151 * meter / second}}] {'ibc1': {'y': 0.00288151 * meter / second}}] \n", + "16600 [0.00205081 * 10.0^0 * ((meter / second) / second) ** 2, [0.00205081 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.5549314e-06 * meter / second}}, {'ibc0': {'y': 4.5549314e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00287196 * meter / second}}] {'ibc1': {'y': 0.00287196 * meter / second}}] \n", + "16800 [0.00199925 * 10.0^0 * ((meter / second) / second) ** 2, [0.00199925 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.6707073e-06 * meter / second}}, {'ibc0': {'y': 4.6707073e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00286368 * meter / second}}] {'ibc1': {'y': 0.00286368 * meter / second}}] \n", + "17000 [0.00197535 * 10.0^0 * ((meter / second) / second) ** 2, [0.00197535 * 10.0^0 * ((meter / second) / second) ** 2, [] \n", + " {'ibc0': {'y': 4.7530243e-06 * meter / second}}, {'ibc0': {'y': 4.7530243e-06 * meter / second}}, \n", + " {'ibc1': {'y': 0.00285702 * meter / second}}] {'ibc1': {'y': 0.00285702 * meter / second}}] \n", + "\n", + "Best trainer at step 17000:\n", + " train loss: 4.84e-03\n", + " test loss: 4.84e-03\n", + " test metric: []\n", + "\n", + "'train' took 16.232710 s\n", + "\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trainer.compile(bst.optim.LBFGS(1e-3)).train(2000, display_every=200)" + ] + }, + { + "cell_type": "markdown", + "id": "9dc20d3bc5b2e106", + "metadata": {}, + "source": [ + "Let's visualize and save the data." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "5c9f7a8ec63d3638", + "metadata": { + "ExecuteTime": { + "end_time": "2024-11-26T08:33:37.376974Z", + "start_time": "2024-11-26T08:33:36.834728Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving loss history to D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\loss.dat ...\n", + "Saving checkpoint into D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\loss.dat\n", + "Saving training data to D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\train.dat ...\n", + "Saving checkpoint into D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\train.dat\n", + "Saving test data to D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\test.dat ...\n", + "Saving checkpoint into D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\test.dat\n" + ] + }, + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "trainer.saveplot(issave=True, isplot=True)" + ] + }, + { + "cell_type": "markdown", + "id": "295c375c641f4943", + "metadata": {}, + "source": [ + "We can also test the model with the data:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "40109d87837d8e20", + "metadata": {}, + "outputs": [], + "source": [ + "def gen_testdata():\n", + " data = np.load(\"../dataset/Burgers.npz\")\n", + " t, x, exact = data[\"t\"], data[\"x\"], data[\"usol\"].T\n", + " xx, tt = np.meshgrid(x, t)\n", + " X = {'x': np.ravel(xx) * u.meter, 't': np.ravel(tt) * u.second}\n", + " y = exact.flatten()[:, None]\n", + " return X, y * uy" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "600622e0fc0ccf2e", + "metadata": { + "ExecuteTime": { + "end_time": "2024-11-26T08:33:39.149077Z", + "start_time": "2024-11-26T08:33:37.402855Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean residual: 0.02894243 * (meter / second) / second\n", + "L2 relative error: 224.70277\n" + ] + } + ], + "source": [ + "X, y_true = gen_testdata()\n", + "y_pred = trainer.predict(X)\n", + "f = pde(X, y_pred)\n", + "print(\"Mean residual:\", u.math.mean(u.math.absolute(f)))\n", + "print(\"L2 relative error:\", deepxde.metrics.l2_relative_error(y_true, y_pred['y']))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/experimental_docs/unit-examples-forward/diffusion_1d.ipynb b/docs/experimental_docs/unit-examples-forward/diffusion_1d.ipynb new file mode 100644 index 000000000..45f0d5ef2 --- /dev/null +++ b/docs/experimental_docs/unit-examples-forward/diffusion_1d.ipynb @@ -0,0 +1,433 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# One-dimensional Diffusion Equation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem setup\n", + "We will solve a diffusion equation:\n", + "\n", + "$$\n", + "\\frac{\\partial y}{\\partial t} = C \\frac{\\partial^2y}{\\partial x^2} - e^{-t}(\\sin(\\pi x) - \\pi^2\\sin(\\pi x)), \\qquad x \\in [-1, 1], \\quad t \\in [0, 1]\n", + "$$\n", + "\n", + "with the initial condition\n", + "\n", + "$$\n", + "y(x, 0) = \\sin(\\pi x)\n", + "$$\n", + "\n", + "and the Dirichlet boundary condition\n", + "\n", + "$$\n", + "y(-1, t) = y(1, t) = 0.\n", + "$$\n", + "\n", + "The reference solution is $y = e^{-t} \\sin(\\pi x)$.\n", + "\n", + "\n", + "\n", + "## Dimensional Analysis\n", + "\n", + "\n", + "Below is the dimensional analysis of the given **diffusion equation** with an unknown parameter $C$:\n", + "\n", + "\n", + "### Step 1: Assign Dimensions to Variables\n", + "\n", + "1. **Spatial Coordinate $x$:**\n", + " - Spatial coordinate has the dimension of length:\n", + "\n", + " $$\n", + " [x] = L.\n", + " $$\n", + "\n", + "2. **Time $t$:**\n", + " - Time has the dimension:\n", + "\n", + " $$\n", + " [t] = T.\n", + " $$\n", + "\n", + "3. **Function $y(x, t)$:**\n", + " - $y$ is the solution of the diffusion equation and depends on the context. For this case, $y$ has no explicit physical quantity associated with it, but we assume it to be **dimensionless** since the reference solution is given as $ y = e^{-t} \\sin(\\pi x) $, where both $e^{-t}$ and $\\sin(\\pi x)$ are dimensionless.\n", + "\n", + " $$\n", + " [y] = 1 \\quad \\text{(dimensionless)}.\n", + " $$\n", + "\n", + "4. **Parameter $C$:**\n", + " - The term $C \\frac{\\partial^2 y}{\\partial x^2}$ must have the same dimension as $\\frac{\\partial y}{\\partial t}$ for consistency.\n", + "\n", + " - First, consider the time derivative:\n", + "\n", + " $$\n", + " \\left[\\frac{\\partial y}{\\partial t}\\right] = \\frac{[y]}{[t]} = \\frac{1}{T}.\n", + " $$\n", + "\n", + " - Next, consider the second spatial derivative:\n", + "\n", + " $$\n", + " \\left[\\frac{\\partial^2 y}{\\partial x^2}\\right] = \\frac{[y]}{[x]^2} = \\frac{1}{L^2}.\n", + " $$\n", + " - Multiplying by $C$, the dimensions of $C$ must satisfy:\n", + "\n", + " $$\n", + " [C] \\cdot \\frac{1}{L^2} = \\frac{1}{T} \\implies [C] = \\frac{L^2}{T}.\n", + " $$\n", + "\n", + "5. **Source Term:** $e^{-t} \\left(\\sin(\\pi x) - \\pi^2 \\sin(\\pi x)\\right)$\n", + " - The exponential term $e^{-t}$ and the sine functions are dimensionless. Therefore, the source term is dimensionally consistent with:\n", + " \n", + " $$\n", + " \\text{Source Term} = \\frac{1}{T}.\n", + " $$\n", + "\n", + "---\n", + "\n", + "### Step 2: Initial and Boundary Conditions\n", + "\n", + "- **Initial Condition:** $y(x, 0) = \\sin(\\pi x)$.\n", + " - $\\sin(\\pi x)$ is dimensionless, consistent with $ [y] = 1 $.\n", + "\n", + "- **Boundary Condition:** $y(-1, t) = y(1, t) = 0$.\n", + " - The boundary values are dimensionless.\n", + "\n", + "---\n", + "\n", + "### Step 3: Summary of Dimensions\n", + "\n", + "| Variable/Parameter | Physical Meaning | Dimensions |\n", + "|------------------------|-----------------------------------|-----------------------|\n", + "| $x$ | Spatial coordinate | $L$ |\n", + "| $t$ | Time | $T$ |\n", + "| $y$ | Solution (dimensionless) | $1$ |\n", + "| $C$ | Diffusion coefficient | $L^2 / T$ |\n", + "| Source term | Forcing function | $1 / T$ |\n", + "\n", + "---\n", + "\n", + "In conclusion,\n", + "\n", + "- The unknown parameter $C$ has dimensions of $L^2 / T$, which is consistent with the physical meaning of a diffusion coefficient.\n", + "- The function $y$ and the boundary/initial conditions are dimensionless, ensuring the consistency of the problem setup.\n", + "\n", + "\n", + "## Implementation\n", + "\n", + "Import the required libraries:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T13:42:57.489721Z", + "start_time": "2024-12-17T13:42:53.900651Z" + } + }, + "outputs": [], + "source": [ + "import brainstate as bst\n", + "import brainunit as u\n", + "\n", + "import deepxde.experimental as deepxde" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the physical units for the problem:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T13:42:57.520303Z", + "start_time": "2024-12-17T13:42:57.494778Z" + } + }, + "outputs": [], + "source": [ + "unit_of_x = u.meter\n", + "unit_of_t = u.second\n", + "unit_of_f = 1 / u.second\n", + "\n", + "c = 1. * u.meter ** 2 / u.second" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the geometry and time domain:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T13:42:57.577592Z", + "start_time": "2024-12-17T13:42:57.573968Z" + } + }, + "outputs": [], + "source": [ + "geom = deepxde.geometry.Interval(-1, 1)\n", + "timedomain = deepxde.geometry.TimeDomain(0, 1)\n", + "geomtime = deepxde.geometry.GeometryXTime(geom, timedomain)\n", + "geomtime = geomtime.to_dict_point(x=unit_of_x, t=unit_of_t)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the initial condition and boundary condition functions:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T13:42:57.589705Z", + "start_time": "2024-12-17T13:42:57.586185Z" + } + }, + "outputs": [], + "source": [ + "def func(x):\n", + " y = u.math.sin(u.math.pi * x['x'] / unit_of_x) * u.math.exp(-x['t'] / unit_of_t)\n", + " return {'y': y}\n", + "\n", + "\n", + "bc = deepxde.icbc.DirichletBC(func)\n", + "ic = deepxde.icbc.IC(func)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the neural network model:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T13:42:58.048271Z", + "start_time": "2024-12-17T13:42:57.611872Z" + } + }, + "outputs": [], + "source": [ + "net = deepxde.nn.Model(\n", + " deepxde.nn.DictToArray(x=unit_of_x, t=unit_of_t),\n", + " deepxde.nn.FNN([2] + [32] * 3 + [1], \"tanh\"),\n", + " deepxde.nn.ArrayToDict(y=None),\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the PDE function:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T13:42:58.061945Z", + "start_time": "2024-12-17T13:42:58.057100Z" + } + }, + "outputs": [], + "source": [ + "def pde(x, y):\n", + " jacobian = net.jacobian(x, x='t')\n", + " hessian = net.hessian(x, xi='x', xj='x')\n", + " dy_t = jacobian[\"y\"][\"t\"]\n", + " dy_xx = hessian[\"y\"][\"x\"][\"x\"]\n", + " source = (\n", + " u.math.exp(-x['t'] / unit_of_t) * (\n", + " u.math.sin(u.math.pi * x['x'] / unit_of_x) -\n", + " u.math.pi ** 2 * u.math.sin(u.math.pi * x['x'] / unit_of_x)\n", + " )\n", + " )\n", + " return dy_t - c * dy_xx + source * unit_of_f\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the problem and train the model:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T13:42:59.334380Z", + "start_time": "2024-12-17T13:42:58.070890Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Warning: 10000 points required, but 10082 points sampled.\n" + ] + } + ], + "source": [ + "problem = deepxde.problem.TimePDE(\n", + " geomtime,\n", + " pde,\n", + " [bc, ic],\n", + " net,\n", + " num_domain=40,\n", + " num_boundary=20,\n", + " num_initial=10,\n", + " solution=func,\n", + " num_test=10000,\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Train the model:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "ExecuteTime": { + "end_time": "2024-12-17T13:43:08.334394Z", + "start_time": "2024-12-17T13:42:59.359833Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Compiling trainer...\n", + "'compile' took 0.066982 s\n", + "\n", + "Training trainer...\n", + "\n", + "Step Train loss Test loss Test metric \n", + "0 [39.28094 * becquerel2, [42.6258 * becquerel2, [{'y': Array(2.4083016, dtype=float32)}] \n", + " {'ibc0': {'y': Array(0.82120794, dtype=float32)}}, {'ibc0': {'y': Array(0.82120794, dtype=float32)}}, \n", + " {'ibc1': {'y': Array(1.7334808, dtype=float32)}}] {'ibc1': {'y': Array(1.7334808, dtype=float32)}}] \n", + "1000 [0.00716378 * becquerel2, [0.03221128 * becquerel2, [{'y': Array(0.08175115, dtype=float32)}] \n", + " {'ibc0': {'y': Array(0.00580588, dtype=float32)}}, {'ibc0': {'y': Array(0.00580588, dtype=float32)}}, \n", + " {'ibc1': {'y': Array(0.00591157, dtype=float32)}}] {'ibc1': {'y': Array(0.00591157, dtype=float32)}}] \n", + "2000 [0.00374766 * becquerel2, [0.01406009 * becquerel2, [{'y': Array(0.0635821, dtype=float32)}] \n", + " {'ibc0': {'y': Array(0.0034853, dtype=float32)}}, {'ibc0': {'y': Array(0.0034853, dtype=float32)}}, \n", + " {'ibc1': {'y': Array(0.00233263, dtype=float32)}}] {'ibc1': {'y': Array(0.00233263, dtype=float32)}}] \n", + "3000 [0.00207005 * becquerel2, [0.00866511 * becquerel2, [{'y': Array(0.04210193, dtype=float32)}] \n", + " {'ibc0': {'y': Array(0.00153627, dtype=float32)}}, {'ibc0': {'y': Array(0.00153627, dtype=float32)}}, \n", + " {'ibc1': {'y': Array(0.00113975, dtype=float32)}}] {'ibc1': {'y': Array(0.00113975, dtype=float32)}}] \n", + "4000 [0.00109155 * becquerel2, [0.00996974 * becquerel2, [{'y': Array(0.02316353, dtype=float32)}] \n", + " {'ibc0': {'y': Array(0.00045823, dtype=float32)}}, {'ibc0': {'y': Array(0.00045823, dtype=float32)}}, \n", + " {'ibc1': {'y': Array(0.00050199, dtype=float32)}}] {'ibc1': {'y': Array(0.00050199, dtype=float32)}}] \n", + "5000 [0.00051956 * becquerel2, [0.01253793 * becquerel2, [{'y': Array(0.01541764, dtype=float32)}] \n", + " {'ibc0': {'y': Array(0.00017889, dtype=float32)}}, {'ibc0': {'y': Array(0.00017889, dtype=float32)}}, \n", + " {'ibc1': {'y': Array(0.00024536, dtype=float32)}}] {'ibc1': {'y': Array(0.00024536, dtype=float32)}}] \n", + "6000 [0.00026679 * becquerel2, [0.01434105 * becquerel2, [{'y': Array(0.01198213, dtype=float32)}] \n", + " {'ibc0': {'y': Array(0.00010253, dtype=float32)}}, {'ibc0': {'y': Array(0.00010253, dtype=float32)}}, \n", + " {'ibc1': {'y': Array(0.00014029, dtype=float32)}}] {'ibc1': {'y': Array(0.00014029, dtype=float32)}}] \n", + "7000 [0.00015957 * becquerel2, [0.01430503 * becquerel2, [{'y': Array(0.00955142, dtype=float32)}] \n", + " {'ibc0': {'y': Array(6.4639426e-05, dtype=float32)}}, {'ibc0': {'y': Array(6.4639426e-05, dtype=float32)}}, \n", + " {'ibc1': {'y': Array(8.0856196e-05, dtype=float32)}}] {'ibc1': {'y': Array(8.0856196e-05, dtype=float32)}}] \n", + "8000 [0.00011952 * becquerel2, [0.01355371 * becquerel2, [{'y': Array(0.00870061, dtype=float32)}] \n", + " {'ibc0': {'y': Array(5.1637177e-05, dtype=float32)}}, {'ibc0': {'y': Array(5.1637177e-05, dtype=float32)}}, \n", + " {'ibc1': {'y': Array(4.7870093e-05, dtype=float32)}}] {'ibc1': {'y': Array(4.7870093e-05, dtype=float32)}}] \n", + "9000 [2.9594898e-05 * becquerel2, [0.01290757 * becquerel2, [{'y': Array(0.00810704, dtype=float32)}] \n", + " {'ibc0': {'y': Array(3.8509617e-05, dtype=float32)}}, {'ibc0': {'y': Array(3.8509617e-05, dtype=float32)}}, \n", + " {'ibc1': {'y': Array(2.8898923e-05, dtype=float32)}}] {'ibc1': {'y': Array(2.8898923e-05, dtype=float32)}}] \n", + "10000 [1.6880738e-05 * becquerel2, [0.01241341 * becquerel2, [{'y': Array(0.00777998, dtype=float32)}] \n", + " {'ibc0': {'y': Array(3.39993e-05, dtype=float32)}}, {'ibc0': {'y': Array(3.39993e-05, dtype=float32)}}, \n", + " {'ibc1': {'y': Array(2.0438354e-05, dtype=float32)}}] {'ibc1': {'y': Array(2.0438354e-05, dtype=float32)}}] \n", + "\n", + "Best trainer at step 10000:\n", + " train loss: 7.13e-05\n", + " test loss: 1.25e-02\n", + " test metric: [{'y': Array(0.01, dtype=float32)}]\n", + "\n", + "'train' took 8.116077 s\n", + "\n", + "Saving loss history to D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\loss.dat ...\n", + "Saving checkpoint into D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\loss.dat\n", + "Saving training data to D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\train.dat ...\n", + "Saving checkpoint into D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\train.dat\n", + "Saving test data to D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\test.dat ...\n", + "Saving checkpoint into D:\\codes\\projects\\pinnx\\docs\\examples-pinn-forward\\test.dat\n" + ] + }, + { + "data": { + "image/png": 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", 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eUqkUERER2Lx5s0dLPO5UPvt6Z7097WXRmihs+ct32FGWhF9tyUFavHv2PoF0kXWFs7ZuW2cBZ8OcXNq6A63yoSjK7fPxND6CESNGXBxTXpnXJGIUPBDxCWAoirKLEuDxeBgdHUV/fz/y8vKQl5fn83jrv387gg/bp706b3f4uHMWH3fO4tINafjttkKXz/dHLDdXPP2dOzoL2LZ1287PMBdZoVDo1kUz0MRnpcrHFa7iI3p7exEeHm4nRhEREXZiZGugC4AdthYKhSTlNQAh4hOAOJvdMZvNaG9vx8LCAjZs2MB+SD1lpcpHpjbgCR/u9bjDP49N4cuuGbx0eTlykrlFdgcby7V1My3LFEXZiVFsbKzTi6Y3F3t/4Enl4wpnDhWOdknLxUcAi78bmUyG2dlZVFRUAABJeQ0wiPgEGI7x1jweDwqFAm1tbYiPj8fmzZtXjJp2xUoVREv/ONaitpjVWXH+CxJsSubhmrpEFGSIl2zSB0rl4+tzcNbWrdVqWTEaGRkBj8ez2y+ybesOpIunPysxgUCAxMREJCYmAnAvPgIAW/GQlNfAg4hPAGE7u8N8CAYGBjAyMoKioiJkZWV5/eFwVvlYrVb09PRg6viUV6/tHTwcmQGOfCrHxYVqnCI2sN5rIpGIbbQ40eHxeIiJiUFMTAyysrLYLjGFQmG3MZ+QkACDweCz5FlfsJqVmDvxEWFhYQgJCcHs7KxdfARzriTldW0h4hMAOJvdYaIJTCYTGhoaEBsb65NjOVYQGo0GUqkUfD4fsrB0AJM+OY43vN1vAT8mA9eXxUOhUKC3txcGgwHh4eHsckwg2t34A9suMceNeYVCAbVaDblcblcZrVV0hC+X3TzFWXxEX18fNBrNivERAAnWWyuI+KwxzmZ3ZmZm0NHRgZSUFNTV1fnUbdm28pmcnERnZyeysrIgTM3G//vLQZ8dx1vebJ3GN0NKPHFRKZpKStDd3Q2DwQCtVsvui8THx7PeaydLiqntxjwjyPHx8VAqlTh+/Di6urqWDYzzN4G0BxUWFsa2ahcXFy+Jj2CqRsf4CICI0WpBxGcNoSgK09PTUCqVyMvLA0VR6OnpweTkJMrKylh3YV/C4/FgtVrR0dGB6elpVFVVITk5GY9+1rcm+z0rMak24bKXJdi0Lg73NEQjJCQE69evt5uel8vlGBwcZJeibNtyTwZCQkLs9kJsl5+YO37btu74+Hi/uHUzrc+BdDG2Xap1Jz5CKBQucewGSMqrvyDiswbYzu5otVrMzc0hJSWFXf5qampCVFSUX45ttVoxOjqKqKgodkZIpjbg5YNjfjmeLzgyqsblE2rcf2oC1q93Pj3v2JbLOAwwldFq3f2vJs6aHxyXn5g7fqVSaXeRtb3j90W1wpxLoFQ+AOyi4x3xNj7CNuXVVoxIyqv7EPFZZRyX2UJCQmAwGHDo0CFkZ2ejsLDQbx/g8fFxzM3NIT4+Hhs3bmSP88r3YwFX9TiiswB371did1cznvlpOVKFP+xrOM6I2HZCDQ8Po6OjY1Xu/lcbdyoNxzv+5WIRGKFerq3bnXMBAqv7jqIot286PI2PYGaHSMord4j4rCKO8dZWqxXHjx+HwWBAXV0d27njaywWC7q6ujA3N4fExES7IcZAr3oc6ZnW4qxnDuP2M3JwdWO20+c4dkLZ3v339PTYDXUGc/MCl2Uux4ssE4ugUCgwNrb4PnA0/3TnGLYhhoEC1w5Jd+IjrFbrEsduIkaeQcRnFXCc3WEsciQSCUJDQxEZGek34VlYWIBEIkFYWBiampowNDRkt1wzotAFfNXjjCf3jWB/vxy/2ZqPinThis+1vft3ltVD07TdflEwNS94c57OYhEYvzVmL83Wt47ZS1tu4BUIvGU3X5yPs9+T7SzWcvERzByRrRiNjY1hYWEBBQUFJ33KKxEfP+MYbw0AIyMjGBgYQH5+PoRCITo7O31+XJqmMT4+jp6eHuTk5CA/P59NkrQ9l6jQ4F1+aj2+gMtelqA4JXrJUtxyLJfVo1AonDYviESiJd55gXKB8MfAq6P55/z8/BK/Ndu9NKatO1CX3fyxvOo4i+VufASz2mGxWNjP4cmc8krEx0/YDrExd2Amkwnt7e3QarXYuHEj2yLrTribJ1gsFnR2dkIul6O2tpbthAIWPzi2x/u00/8+bv7GnaW45bBtXmAuuEzzwuTkJNu8wFxsmb26QMDf3WVM5EF8fDxyc3NhtVrZvTSmrZtxFWAypALpYrlag8mexEcws1DMMhywcsrriSxGPDoQPEtOMJzFW8vlcrS3tyMhIQFlZWXsRuj8/DyOHj2KM8880yfHZpbzIiMjUVlZuWTgsL+/H0ajEeXl5ZCpDdjy5LdBuey2HGVp0fjv7YUul+LchWleUCgUUCqV0Gq1EAgESE9Ph0gk4uxI7QukUinEYjEyMjLW5Pi2bd1yuRx6vX7ZQc61oLm5GZmZmUhJSVmzcwBgFx8xMTEBo9Ho1LGbERZGjGxvEi+99FJceeWVuPTSS9fqx/A5pPLxMc7irfv6+jA2NoaSkhJkZGTY3b24G2vtCpqmcfz4cfT29iI3Nxf5+flO75JsK59g6HLzlM4prcdLcSvh2LzQ39+P+fl5mEwmu5ZcpjJazeaFtZ6rsW3r1mg0OHbsGNatWwelUskOcsbGxrK/G6ZDbLUIFEsm2/gIo9EIPp8PsVjsUXyETCZbUyH3ByfWT7OGOLPI0ev1kEqlsFqtaGxsdOrD5QvxMZvN6OzshFKpRF1dHesE7AxGEIOty81TmKW4c8vEuO2MfK9FiEEgECAyMhKlpaVs8wJTFY2Njdk1L4hEIjsTUF8TSIsWNE0jJCQEKSkpbKWxUlv3agh1oIiPLVarld03cxUfkZCQAIVCgbS0NOh0Oo9n/77++ms8/vjjaG5uxtTUFN5//33s2rVrxe85cOAAbr/9dtb55N5778VVV11l95znnnsOjz/+OGQyGaqqqvDMM89g06ZNHp0bQMTHJzizyJmenkZHRwfS09NRVFS07B0fIwZc72LVajUkEgmioqLQ1NTk0teL8XYL1i43T/mkcw6fdM5hR1kSbj0jz2ciBNg3Lzh2i83NzbHNC8ydP5NB4yvWuvKxxdm5LNfWbSvUjh1ivvx5mNWHQMJZE8RK8RGvvPIK3nrrLfB4PDz//POYn5/H6aefzs5trYRWq0VVVRWuueYaXHTRRS6fPzw8jB07duDGG2/Ea6+9hr179+K6665DWloatm3bBgB48803cfvtt+P5559HfX09nnrqKWzbtg29vb1sXpW7kD0fL3Gc3aEoCt3d3ZienkZZWZnLN4nJZMK+fftw1llnebQkwbRt9vX1IT8/H7m5uW59cEdHRyGXy9GiE+HxVc7uCQTcDa9bjuHhYej1epSWlrp8rtVqxfz8PFsZLSwssBk0IpHIa9+15uZmZGRkuHUh8jcqlQqdnZ3YvHmzW8937BBTqVR2w8IrtXW7y7fffouKigrExQVOTpRUKkViYiIyMzPd/h65XI6ysjJceOGF6OrqglQqxbXXXou//e1vbr8Gj8dzWfncdddd+Pjjj9HR0cE+dskll0ClUmHPnj0AgPr6emzcuBHPPvssgEUxzcrKwi233IK7777b7fMBSOXDGdvZHcZQkXGIFggEaGpqcstfjLkz86Qt1Gw2o6OjA2q12uNgOR6PhzmdFX/+8uQTHmAxvO6zrlm8eW2dT6sgZ9jOyADL+64xlRGX5oVAqnw8qTKcdYgtLCxAoVAsaevmWjUG6rKbp39jkUgEs9mM+++/H+vXr4dCoYBCofD5uR06dAhbt261e2zbtm249dZbASzeKDc3N+Oee+5hv87n87F161YcOnTI4+MR8eGAs3hrZrPfdqbGHZjnWa1Wt+6CVSoVpFIpYmJi0NTUZBe45u7xphYsoE7ielehs+CsZw7j+s1Z+OWW3FU7rjPfNaYq6u7uhtls9sjqJpAWLbyNU7DdlGfaum2TS3t6eli/PuZ/rt77J4r4mEwmmM1mds/YdonOl8hksiWdgSkpKZifn2f376xWq9Pn9PT0eHw8Ij4e4Cze2mKxoKOjAyqVaslMjTswH1hXTQc0TbPDqQUFBcjJyeH0YefxeEiOBHjASbHnsxIvfHcc77ZO4vfnFWFLoX8cJlYiPDzcLk7bcU8EgF1shGPzQqDt+fjyQu9sH4SpGkdHR9HZ2Yno6Gj2d+PY1s18VgNNfLgMvmo0GgAIqOBAX0DEx02cze4wVUhsbCw2b97scRXCvI6rjjdmOHVhYYEdTuUK0+BAWEShs+KWt7oQFxGCv15a4dZ8kD8u+MtZ3dgmmIaGhtp10vnrXLjg7yA5x5Z3k8nEipFtW7dtJx0QWHY/ALcmCI1Gwza3+JPU1FRMT9sPnU9PT0MoFCIyMpL1rnP2HC77jkR83MBxdgcAhoaGMDQ0hMLCQqxbt87rJYflxEepVEIqlUIoFHJaZrNFpjagdVKLfw0YTvqqxxG1wfp/80FReOanFX7fD3KFrdVNTk6O3TLU+Pg4uru7wePxMDm5mDy7mqFxzljtKiwsLAzJyclshxWTz8MsYTIxB+Pj40vMdNcSLstuTJu1v8+/sbERn3zyid1jX3zxBRobGwEs/s7r6uqwd+9etnGBoijs3bsXN998s8fHI+KzAs5md4xGI9rb26HX67Fp0yafdNI4Ex+apjE8PIzBwUGfCNzbzRO4/8Puk3qvxx16pnU465nDOKNIhHvOLlxzEWKwXYbKz8+H2WzGkSNHAIBtXnDM6VnNgc61TjG1zeehaRrz8/Nobm6GTqfD5OQkm3zrr7Zud+EiPhqNhpPZrUajwcDAD41Fw8PDkEgkEIlEyM7Oxj333IOJiQm8+uqrAIAbb7wRzz77LO68805cc8012LdvH9566y18/PHH7GvcfvvtuPLKK7FhwwZs2rQJTz31FLRaLa6++mqPzg0g4rMszmZ35ubm0N7eDrFYjJqaGp9NHDuKj8lkQltbG7RarU8ETqY2EOHxkH29CuzrPYwz1otwz7YfRChQliyZ0LLMzEwkJiba3fl3dXWxA522zgv+vNj6e9nNE3g8HjvvVl5eDgB2LtSM8adt84I/h4EZmH0oT8VHq9Wy3nmecOzYMZx++unsv2+//XYAwJVXXondu3djamqK3VsEgNzcXHz88ce47bbb8D//8z/IzMzE3//+d3bGBwB+9rOfYXZ2Fvfffz9kMhmqq6uxZ88eThZGRHycwGS3M9UOTdPo7e3F8ePHUVpa6nMvLVvxUSgUkEqliI+PR1NTk0+WUkYUOiI8HNnXp8C+Pm6mpasBc8F0vPO3zekZHR0FALv9Im9naBxZ68rHEeazy/yMti7Utl5rzH7aasSwM5/x1ap8tmzZsuLN0u7du51+T2tr64qve/PNN3NaZnOEiI8NtvHWzIdJp9NBKpUCAJqamjjdgbiCsVofHBzE0NAQ1q9fj+zsbJ9dHHJEUeDzQATIC57cN4KPOqZxRlYYqpICI4ZiuX0Wx+YFxmWZaV7o7+9fNhqBK4FU+QArt1nbtnUz+2lMdISjvQ3zO/Jmr5XBdhXFE3Q6nV+uO2sNEZ//g5ndOXbsGDIyMpCSkoKpqSl0dXUhIyMDRUVFfruz4/F4GBgYgNVqRX19PYRC3zgyM6TGReD35xXj/g97SKOBF/TN6NE3owcAXDrX75VTgi9wdwmQz+c7bV5gwvS6uroQHR1td+fv6ZJyILV9A57N+DgOAzP2Nky6q+Pvh2tzB1fxYSqfE42TXnwcZ3csFgvrIDAzM4PKykqPPYs8QS6XQ6PRQCgUor6+3i/OtUajETnUJO7ZGIpHjpp9/vonI6vplLAcXC/4jjM0ZrOZ3Q8ZHByEXq9n25aZ2AhXF8xAm6nxxtdNIBAgMTGRndlz/P0wzhS2YuTOUhrTbODp30yr1Z5wMz7ASS4+jvHWzJuiv78f0dHR2Lx5s0+NIB2PPTAwgJGREdaY0h/CI5fLWT+pM5tK8cej35Pqx0cwTgmOTQmriS+qjdDQUKdtywqFAp2dnbBYLGynmEgkctopFsyVjyscfz9Go5EVo56eHphMJrbTUCQSLdvWzTVZVafTEfE5kbCd3WGSBcfGxqBUKiEWi1FXV+e3D5PBYEBbWxuMRiMaGhrQ19fn8y4qmqbZWaTi4mJkZmbi8IiSCI8fYJoSVrs9218XfGfNC4wN0MjICNspxuwXRUZGBmzDgT8IDw9HamoqUlNTQdM0DAYD+/uZmJiA1Wq1a+tmOg25VmNcu90CnZNOfJzN7jDLbPPz80hMTERCQoLfhGdubg5tbW0Qi8Wora2FQCDwWaAcA9OqrdPp7PaQOibmfXYMwlKY9uz6nDj86vRcn6WpLsdqtH3bNi84dorZGoAKBAKEhYXBaDR63bzgC1YzQjsyMhIZGRnIyMgATdN2bd1Mp2F8fDzCwsLYSBNPri8ajYZ1bDiROKnEx9nsjlKpRFtbG+sg0NfXx37dl1AUhYGBAYyOji5JNPWl+DCOCHFxcWhsbGQ3RmVqw0nrZL3aHB5R47KXJdi0Lg4v/keV346zFktdzjrFVCoVhoaGoNFo8N1337Gb80xsxFokcK7VHhSPx7Nr67bNeJLJZNDr9fj222/tKseIiIgV/45arRZpaWmr+FOsDieN+DjO7gCLk+HDw8N2rc0hISE+rUKAxWU2qVQKs9mMhoaGJXcxTKu1N9A0jdHRUfT39zt1RCCzPqvPkVE1Nj32NW4/Mx9bCsV+WY5b632WkJAQJCYmQi6XIyEhgY3RtvVcc3ReWA1RCJQGCFubpLCwMExNTSE3N3fZtm5nbe9cUkyDgRNefJzN7hiNRkilUphMpiWtzSEhITCbfdcRNjs7i7a2NiQnJ6OkpMTpXaC3lY/ZbEZ7ezvm5+eXNR4lsz5rg94M/GHPIP6wZ9DnaaqBtMnPbKY7a15g9kOYKG1bp25/2dwEivjYYrVa7YZZmccYg1Sm7T0qKgoJCQmgKAqJiYledbt5Enm9ZcsWfPXVV0seP/fcc1mLnauuugqvvPKK3de3bdvGhs15wgktPs6W2WZnZ9He3o7k5GTU1dUtEQNfVCHA4pu/v78fY2NjLl0RvBEfJkbbVb7PNwNyBIgzzEnLx52z+LhzFheWxeP+80q9Xo4KFKsfYHmHg4iICKSnp7NR2sx+iEKhwPDwsM/TSxkCVXwcz4mpHG3buhkxevHFF/H3v/+d3VPLz8/Hqaee6rYQeRp5/d5777GGrMBip2xVVRUuvvhiu+dt374dL7/8Mvtvrnt8J6z4OMZb0zSNnp4eTExMoLS0FOnp6U6/zxfLbnq9HlKpFBaLBY2NjS7fLHw+n233dheaptkAO1cx2oy3W+Bcqk5u3u9U4cPOb3FlWQQuqExesT13JQKt8nF1Lo77Ic7SS5klKKYy4uosEKji46rV2jZw8IknnsAvf/lLbN++HWazGTfffDPGxsZwySWX4P/9v//n8nhPPvkkrr/+etb08/nnn8fHH3+Ml156yWnktWNA3RtvvIGoqKgl4sN0+3nLCSc+jrM7fD4fWq0WUqkUPB4PTU1NK66fhoSEeFX5zMzMoL29HSkpKSgpKXGrr9/TysdisaCzsxMKhQJ1dXUuUw3Jfk/gYQEfL3aa8Gr3OK4rHkeZiLazc3HX6DJQxIdLq7Wz9FJPAuNWgutMjT/hck5ZWVmIiIjAr3/9a5xzzjkYGRlhYzRWwheR1y+++CIuueSSJW3eBw4cQHJyMhISEnDGGWfg4Ycf9jhEEzjBxIeZ3bG9kE9OTqKrqwtZWVlYv369yw8I12U3iqLQ29uL8fFxlJeXe9Sd4on4LCwsQCKRICIiAk1NTW6VvDmiKJJcGqCYKeCvXUBMWAh+XsVDkWYGIYODbHAc40TgrAIItGU3b4XQcQmKCYxTKBRLmhdcVYuBWvlwWWq1bbXOyclBTk6Oy++Zm5vzKvL6yJEj6OjowIsvvmj3+Pbt23HRRRchNzcXg4OD+O1vf4tzzjkHhw4d8lhYTwjxsbXIYd50VqsVnZ2dkMvlqK6uRlJSkluvxWXZjTEfpSiKk/mou+IzMTGBrq4u5OTkoKCgIGDuegneozFR+OtRJQBgS2EibmpIhsC0YOe9xghRfHw8e2ENlPeAP4xFHQPj9Ho920nX3t6+YkYPRVFr0uK9ElarldMy4lrY67z44ouoqKhY0pxwySWXsP9dUVGByspK5Ofn48CBAzjzzDM9OkZg/XU44KypYH5+HlKpFJGRkWhqavLIIsfTZTeZTIaOjg6kp6ejqKiIU6nvSnysViu6urowMzODmpoaNkrYXUYUOlL1BBEH+pU40K/EzspkPHz+RphMJvai29vbC6PRyGY8aTQahIeHr7kIrYbDQWRkJCIjI+2aF5hOOsfmBZPJ5BMnal/CJUiOcZjw9IZWLBZzjrzWarV444038OCDD7o8Tl5eHsRiMQYGBk4u8XEWbz0yMoKBgQHk5eUhLy/P4w+lu8tuFEWhp6cHk5OTKC8v92oDbqVqS6PRQCKRQCAQcPaaI84Gwcm/2mbwZfccfnfeelRnxqM4JQU0TUOv10Mul0OlUqGzs9Op3c1qi9FqRyrYNi9kZ2eDoig2FkEmk7GR40ajkRWktRYjLns+BoMBVqvVY4cDbyKv3377bRiNRvzHf/yHy+OMj49DLpdzGoINSvFZziKnvb0dCwsL2LBhA9tH7ynuLLvpdDpIJBIAcNnA4A7LVT5TU1Po6OhAdnY2CgsLOd1ZEmeD4EZrpvCb9xfX6C/dkIbfbitEVFQUwsPD0d/fj8bGRnaWxrZjjBEikUjkk0BCV6x15x2fz0d8fDzi4+ORm5uLtrY2hIWFISQkhG1eiImJsXPqXu1lOS6Vj1arBQBOy26uIq+vuOIKZGRk4I9//KPd97344ovYtWvXkiYCjUaD3//+9/jxj3+M1NRUDA4O4s4770RBQYFd2qm7BJ34OFtmUygUaGtrQ0JCAjZv3uzVh83VstvU1BQ6Ozt9mvHjKD62VVVVVZVXkQ6k0+3E4Z/HpvBeyxRuOG0ddpQsLr3aTtDb2t0wCaadnZ1L4hH80QUWaMaiNE0jNjaWna9ztnQpFApZkebS6u4pXIxFtVot+Hw+p2RVV5HXY2NjS86nt7cX3377LT7//PMlrxcSEoK2tja88sorUKlUSE9Px9lnn42HHnqI06xPUImPs9md/v5+jI6Oss7N3t59LbfsZrVa0dPTg6mpKVRUVHDKLF/pmIz4+LqqIs4GJxZGCnjmwCieOTCKing+iqpNyBD9cLPl2DHG2P8rFAp0d3fDbDYjLi6ObV7wlcNAoCWZOl7ow8LCkJKSwn5umeYFhUKB8fFxu+YFkUjEKbbanXPiUvl4cy4rRV4fOHBgyWNFRUXLdlFGRkbis88+43QezggK8bGd3WHusBi/NIvF4tQvjSvMspvtMoJWq4VEIgGfz/eJIDjCiM/MzAza2tqQnp6O4uJin9yJEWeDE5d2FR/b/9qM6sxY3HlWvlMXbUf7f8d4BGaTnhEjrvlVgVb5uGq1dmxe0Gg0bGVk27xgu4/mLVzEh0kxDSRh9xUBLz5MvLXtMtv09DQ6OjqQlpaG4uJiny4jMK/FbA5OTk6is7PT7TkhrjB+c57OCK0EcTY4OZCML+CylyWoSI/Bkz8uW9Y7zlk8wvz8PBQKBWtyGRERYdfS7e4SdqBVPp7M+fB4PMTGxiI2NtauecHx92Lr1M2leYFLw8GJmuUDBLD4OMZb83g8UBSF7u5uTE1Ned1hthzMG9ZkMmFwcBDT09Ne77ushMFgQE9PD6xWK0455RSfvtHIfs/JRfukBmc9cxg1WbH4zVbnlZAttpv0wKJzhrM4bebufyVH6rVuOHDEmyFTZ78XxnlhZGQEGo0GMTExds4L7sZoc9nzIZXPKkLTNObn57GwsIDExETweDx26UsgEPhl6YuBeRMdO3YMoaGhaGpq8knJ7Yy5uTlIpVIkJCTAYDD4/A6nfVzt09cjBAetxxcroXxxJJ6/tNJtF22BQMD6igH2cdqTk5NsQidz0bW9KAaao4Avz0cgEEAsFrPzdUzzgkKhsJu7Yiqj2NjYJcdmbqZJ5fMDASc+TLWjVCoxNDSEpqYmjI+Po6enB+vWrUNBQYFf3+SMb1JCQgJKS0v9ciyapjEwMICRkRGUlpYiLi4OBw8e9OkxRmfn8ecvB336moTgYnBOj7OeOYychAj8+qw8bCn0bDjZMU6bGeqUy+UYHByEQCBghSgQl9385e1m27zAzF0xFaNt84KtSDPbBlz3fE5EAkZ8HGd3QkNDYbFYIJVKoVQqUVtby8m8zl0sFgu6urowOzsLPp+PdevW+UV4mL0do9HINkrodDqfBtgplUp8+k0r2eshAABGlAbc8lYXIkKB6zevwwUVqR5nCjkb6lSr1VAoFJiYmGDNbhMTE9c0wZRhNWO0o6KiEBUVxcZoM80LtiLNOFKYzWaPRkHWwlpntQgI8XE2u6PX66HX6xEdHe22gSZXGLPOsLAwbN68GYcOHfJLlLZCoYBUKoVIJEJtbS374WQ+JN5+YJg00yMd/YhMSAOfJyN7PgQWg/mHNm1mYJUrtlY2ALB//35kZmZCp9PZmYAyzQvOlqL8yVrGaDs2L6jVaszMzAAADh8+zDZ1ML+/lcSIi7VOsLDm4uMs3np4eBgDAwPg8Xioq6vzWzlP0zQmJibQ3d2NnJwc5Ofng8/nex2r4Ow4Q0NDGBoaQlFREbKysux+Jl+Ij8ViQXt7Oz7uVuK1Ph4oWuaTcyecmPzz2BQ+kMhw3SnZnCohZyQmJiIrKwvA4hwN09J9/Phx0DRt17rsbmQEF5j9lUDYg2JEOjQ0FDKZDJs3b2abF4aHh9HR0cEOATtrXmCaG05E1kx8nMVbm0wmtLW1QafToaqqCq2trX47PrNMIJfLl5h1+irNFFjcnGxvb4dGo8GmTZvY8tsWW/HhwsLCAlpbW6FDOF7ro0i1Q3ALvYVmK6Ez1otwz7ZCTiJE0/SSOZ/IyEhkZGSwS1FMaNzs7CwGBgYQGhpqZwHkS981ZkgyEMSHgZnxcWxeYIaAlUolenp6YDKZEBcXxwbtMU1XXPAkQnv37t2s7Q5DeHg4DAYD+2+apvHAAw/ghRdegEqlwubNm/HXv/4VhYXcKug1ER9ny2xyuRxtbW1ITExETU0NeyH2x8bh/Pw8m4mzefPmJUt6vkgzBQCVSgWJRAKhUIimpqZly2tvxIeZQ8rJycFciAgU7T/BJpy47OtTYF/fYRSII/GrM3I9ak5gLvbLVTLOLICY/aKxsTF0dXVxal1eDuZzFIji44jjEDDTvPDpp5/igQcegE6nQ35+PrKzs3HmmWeitLTUrYrR0whtABAKhejt7WX/7Xicxx57DE8//TReeeUV5Obm4r777sO2bdvQ1dXFaTh5TcSH+aF4PB5omkZfXx/GxsZQUlKCjIwM8Hg8Vpi4TAUvh230dG5uLvLz853+Ib1ddmP2Xvr7+1FYWIh169at+Ibh8/nsHJO7MP5vU1NT7BxSrNpArHQIXjEwp8ctb3UhKoyPR3cVuyVCnlYaISEh7F4QYN+63NPTw1oA2bYue7JEF4ji485NtG3zwnXXXYerr74a5513HuLi4vDJJ5/g7rvvRl5eHtrb213+PjyN0GaOv9zsJE3TeOqpp3Dvvfdi586dAIBXX30VKSkp+OCDD+xyftxlzZbdbOOtKYpCY2Oj3dom88axWCw+KcnNZjM6Ozvd6pzzZtnNbDajo6MDarXaI3dtT9JM9Xo9JBIJaJpGY2MjO/OUGheBB88vwX3/Jq4GBO/QmSjc8lYXIkN5eOzCkhVFiHnfct3Dcda6rFAoWHNUHo9nt0Tnau6O+ewGUus3lwHTkJAQhIeHY8eOHfjFL34Bo9GIwcFBlz8X1whtjUaDdevWgaIo1NbW4pFHHkFZWRmAxX14mUyGrVu3ss+Pi4tDfX09Dh06FFziMzU1xfqYOQth4/F4EAgEPtl7UavVduFyrjrnuC67zc/Po7W1le3Q80Q03RWf2dlZtLW1ISUlBSUlJUt+bxfXZSA6LAS3vdPh8fkTCI7ozTRueasLwvAQ3HJ6DrYUipfsC7ladvME27v/zMxMdu/DWWQEI0iOy9lMs0GgiQ+XFRzbVuvw8HCUlpa6/B4uEdpFRUV46aWXUFlZCbVajSeeeAJNTU3o7OxEZmYmZDIZ+xqOr8l8zVPWtOHAlTu0L5a/xsbG0NfX51G4nKfHtV3O8ybEbiXxoWkag4ODGB4eRklJCTIzM5d9bm12PFl+I/iUeaMVf9gziD/sGURDThx+eXoua9/jzw1+Pp+PuLg4xMXFITc3187qxrZbjBEjZrM+kJbcAO7is1qt1o2NjWhsbGT/3dTUhJKSEvzv//4vHnroIb8cc83EJyMjAxaLZcXneCM+zPKXSqXyOFzOkyUw2645bwZhVzqmbRdgfX09hMKVPbuIkzXBn3w/osb3L0uQlRCOR3eVoCBhsfJYjUrDWbcY09Ld2dkJi8WCmJgYtsPOV5ER3sKlcYpxlfDUsd+bCG2G0NBQ1NTUYGBgMYiS+b7p6Wk74+Pp6WlUV1d7dH4MgXV74IBAIHApUM5QqVQ4ePAgKIrC5s2bPU41dVf0FhYWcOjQIRiNRmzevNkrB4bl9pnUajUOHjwIPp+PxsZGl8JDnKwJq8VxpRGXvSzBOc+34FsZH7J546qfQ3h4ONLS0lBaWorNmzdjw4YNiI2NBU3TaGlpwbfffovOzk5MTk7atQ2vNlz2fABuDge2EdoMTIS2bXWzElarFe3t7azQ5ObmIjU11e415+fncfjwYbdf05E1HzJdCS7LXyMjIxgYGEBBQQFycnI43fXw+XyXojcxMYGuri7k5OSgoKDAJyF2tiFOtkt5+fn5yM3NdesYxMmasNrIdVa8PczH288cRn1OHH5lsyS3mjAWQGKxGEqlEps2bWKjESYnJ9Hb24vIyEg7d4HVsgDyxZ6PJ3gaof3ggw+ioaEBBQUFUKlUePzxxzE6OorrrrsOwOLv9tZbb8XDDz+MwsJCttU6PT0du3bt8vj8gDUUH1/vvTDDnAsLCx4vszk7rtHo/C7OarWiu7ubLTcZB2BvsV12s1qt6OzsxNzcnMdLeTmiKPAAUvkQ1oTDI2pOjtq+hFniso1GyMvLYyMjFAoFGxkhFArZLjp/RmlbrVaPPN2AH5bduOz5eBqhrVQqcf3110MmkyEhIQF1dXU4ePCgXYPDnXfeCa1WixtuuAEqlQqnnHIK9uzZwzmAkEcvl5nqZxj36pVobW1FfHw8cnNzV3yeUqmEVCqFUChEeXm5163Zw8PDUKvVS9YymViHkJAQVFVV+TRq4fDhw8jMzER8fDxaW1sRGhqKqqoqj/+wMrUBW578logPISBoyovH73cUraoITU9PY3x8HHV1dSs+z2AwsC3dSqXSzo1aJBL51AKoq6sLUVFRyMnJcft7NBoN0tPTMT097bc8sbUkoJfdXLVa0zSN4eFhDA4OujXM6S7OKi6ZTIaOjg5kZmb6JdGUz+dDpVKhu7vbq2OMKHREeAgBw8EhFc565jDqsoW4pC4d1Zlxfhcid7vdIiIikJ6ebhelbRsZERoaaudH5425MZdlN61WCwDE283XeLvsxnSAabXaZT3TuGK7BMY4CUxOTrpsDecKRVHQ6XRQKpWorKz0KqE1RxRF2qwJAUfz2Dyax+YBADvKknDrGXl+EyEurda2btTr1q1jLYAYY9Suri5ER0fbRYx7IiZcU0yZQdMTkYCufJYTHyaaID4+fkXPNG+Pq9PpIJVKQdO039JTDQYDpFIpzGYz1q1b53U0OGmzJgQ6H3fO4uPOWb8tyflizsfWAig/P58NuHRML2WqIqFQuOINNdfKJzo6OuBmlnxFQIuPQCCw2/i3jSZYv349srOz/dLDzzQcHDp0CGlpaU4dGHyBQqGARCKBWCxGWFiY1503pM2aEEwwS3LrkyPxux1FPuuQ49rWvBKhoaFITk5m916YlQrGHBUA20HHWADZXpu4zPmcyHEKQBAtuxmNRrS1tUGv1/t8mc0WiqIwOTkJvV6PyspKpKen+/wYti3hTL5PZ2en107apM2aEIz0zehx2csSxEXwcV5FKnaUJ3slRKvhcOCYXspYAM3MzKC/vx/h4eF2+0XeVD4nKgFd+TDiw8QtJCQkoKamxm+9+cwSmMFgQFhYmF+Ex9Z4dOPGjYiPjwfgmavCcpD9HkIwozZQeO3oJF47OulVq/Zq2+s4i4xQqVSsMWpnZyd4PB6mpqYALBpyuiNEOp3Or6F7a82aig8TqbAcfD4fGo0GLS0tKC4uRmZmpt/+EHNzc2hra0NSUhLWr1+PlpYWnx+DCX2LiopaYjzqaaSCM/Z2TRLhIZwQDM7pcdYzh1GRHoMnf1zmkQittbdbSEgIEhMT2fk8k8mEgwcPsjOCTGQEs6e0nAUQWXZbIwwGA0ZGRmA0GtHU1OSxv5G70DSNgYEBjIyMsIadGo3GJ2FytjCOCMvlCIWEhLice1qJjqFxPLRnyNvTJBACivZJDc565jByEyNw2cYMp67ajlAU5fMmJG9gbjILCgoQGRlpt180MjLCRm0zS3TM/OCJvuwWkG0Uc3NzOHjwIMLCwhAREeE34TEajTh27BimpqbQ0NDAOkUzy32+mL9l3Ap6enpQXV29rBUP12U3mqbR39+Pr5pJowHhxGVYbsAf9gzirGcO46d/b8aB/rlln7vWlY8jNE2zDQc8Hg/R0dHIzMxEZWUlTj31VFRWViI6OhpTU1P4/vvv8emnn+Kaa67Bt99+y1lEn3vuOeTk5CAiIgL19fU4cuTIss994YUXcOqpp7INE1u3bl3y/Kuuugo8Hs/uf9u3b+d0bgwBtexGURQGBgYwOjqKkpISREdHQyKR+OXYTLu2s30kZj3W2whvnU4HiUQCHo+HpqamFR0RuIiPrdv1ts01eLZTQpbdCCc83dNa3PJWF2LC+fjjzqVpq4EmPkzTlLNzchYZ0dPTA4FAgC+++ALz8/NoaGjAWWedha1bt+KUU05xeU3yNEL7wIEDuPTSS9HU1ISIiAg8+uijOPvss9HZ2YmMjAz2edu3b8fLL7/M/tvb+aOAWXZjNvtNJhMaGhoQGxuLhYUFTq7WK2HrisB0mjlWIsybxBvxYULfUlNTUVJS4vLD4Kn4MMF1sbGxaGxsRGhoKC6oTMMH0ilO50sgBBsa42LaalQoD7edmccuyQWq+LhzLREIBCgvL8ff/vY3/Pa3v4VarcaZZ56JL774Atdeey26urpcvo6nEdqvvfaa3b///ve/491338XevXtxxRVXsI+Hh4d7PYdoS0CID3OhTk5ORl1dHVuFMPY6NE37pNGAMR/VaDQrtmszf1yuZoDMHlJpaandncNKeCI+zP6RbXCdTG3Av9uI8BBOPnRmmg26KxBH4oJ1NM5ODCzx4fF4HguiRqNBSkoKrrzySlx55ZVufQ/XCG1bdDodzGYzRCKR3eMHDhxAcnIyEhIScMYZZ+Dhhx/2KkZmTcWHpmn09vZibGzM6YXaV8tfwGLGj0QigVAodOmKwKxpehpkZzKZIJVKodfr2erNXdwRH8bqZ2pqaomj9skx40MDODHbTgm+YWBOjyfngGdaB/HL0624qiF7rU+J8/VLp9N53O3GJULbkbvuugvp6enYunUr+9j27dtx0UUXITc3F4ODg/jtb3+Lc845B4cOHeJ8bV5T8eno6IBSqURjY6PTX7JtBcL1B6RpGqOjo+jv7/co4yckJMSjZTBG3OLi4tDU1OTxLNJyYXIMBoMBEokEFEWhsbFxidXPyTHjQ4SH4B5mCvjz3hE8uXcE20rEuKIhc00yhgDujgurFaFty5/+9Ce88cYbOHDggJ2j/iWXXML+d0VFBSorK5Gfn48DBw7gzDPP5HSsNRWfwsJChISELCssfD4fPB4PFouFU0yCN1Ha7mYJ0TSNsbEx9PX1eR1gt5zYMTY8SUlJKC0tdfr7Ip5uBMJSaAB7uuewp3sOseF8/OasfFxYleby+3wJ15tnLnM+3kRoP/HEE/jTn/6EL7/8EpWVlSs+Ny8vD2KxGAMDA5zFZ00XRiMjI1f8o/B4PI/TTBnm5+dx6NAhWK1Wv0VpWywWtLW1YWhoCHV1dW6njTrDmfgwNjzNzc0oKChAeXm5098X8XQjEFyzYKRw/0f9qPrD13jwk75Vi/3mKj5clt24Rmg/9thjeOihh7Bnzx5s2LDB5XHGx8chl8vZmG0urHmrtSu4RGmPj4+jp6fHbkPeU1ztwWg0GkgkEoSGhqKpqcnrtkPH41ksFnZZ0taGxxknx34PgeAbKABvt8rwdqsMqTECXNO0DqcXuR5e5Yo3Edpclt08jdB+9NFHcf/99+P1119HTk4OZDIZgMUcoZiYGGg0Gvz+97/Hj3/8Y6SmpmJwcBB33nknCgoKsG3bNo/PjyEgut1WIiQkxO12a4vFgq6uLk7x086Ou5zoyWQytLe3Izs7G4WFhT5p67QVH61Wy6aZuiNsHRPzXh+fQDgZkWkseOTzQTzy+SDWxYXili3ZOLss3ac2Xlxav5kIbS4D9p5GaP/1r3+FyWTCT37yE7vXeeCBB/C73/0OISEhaGtrwyuvvAKVSoX09HScffbZeOihhzy+6X711Vdx2223YXJycu1itIHFOwJXwnLw4EHk5+e7DHGzrUS4xE87wsRa23bgURSF3t5eTExM+DxYTq1Wo7m5GeXl5Whra3M7zVSmNuD0v3xLKh8CwSfQCOfx8PPKaGwtTcX6rGSvrXqOHz/OBkW6fRY0jYKCAvz73/9GQ0ODV8cPJPR6PdLS0vDCCy+cGMtuk5OT6OzsxLp161BQUOCTSsSx243pNrNarWhsbPR5FwqPx4PZbIZUKkV5ebnba6lkyY1A8CU8GGng71It/i4dxPq4fvysJBIbcpMgEokgFAo9vr54s+dzonm7RUZG4rLLLsPLL78c3MtujEvs9PT0krkXXxyXET25XA6pVAqxWIyysjKfB8uZTCZ0dXWBpmmP54Pcb7EmMzIEgqf0qfl46Hsj0ton8PPCcWTH0KwJqLPQOGdwER+KoqDVak9IV+vrr78eGzduDA7xcVb5aLVaSCQS8Pl8l75pXODz+bBYLBgaGsLg4KDfIh0YmxxmbseTN5tMbcCIQoezS5Kxp2vGxbOJ8BAIXJnS0nhMAjTmxOG/c+IwOzvLhsYxQpSQkOB0iY7LkKlWqwUAv5kqryU1NTWoqqoK/GU3xmLHFplMho6ODmRkZKCoqMgvPk48Hg+Tk5OgKMpvyam2NjkZGRk4cOCA21ZCbzdP4P4Pu8mSG4Gwihwamccdeiue+Wk5KqMFbGjc8PAwOjo6IBQKWTFilui42HQx4nOiLbsxXHfddcFV+dhu+JeXl/vU5M6W+fl5zMzMsN1mXAZcV4KiKHR3d0Mmk6GmpgZisZjN8nGnM4aZ6yHCQyCsPj3TWpz1zGHcfkYOrm7MZrtqjUYjFAoFFAoF2tvbQVEUEhISYDQaER8f75FHpU6nQ2hoqNcjHIHKZZddFhziY7FYoNfrIZFIQNM0mpqaltjL+Irx8XF0d3cjNjYWMTExPhceg8GA1tZW0DRtZ5Nj66TtCtJkQCCsPU/uGwHAw9WNWQAWXZ/T0tKQlpYGmqah0WigUCgwNjaG8fFxzM7OulyiY9BoNIiOjj5hI7Tj4uKCY9lNrVbj4MGDSE1NRXFxsc83/AH75oWamhqoVCro9XqfHmMlmxxPxCe4fNxIowPhxOXJfcPYsC5uiW8cj8dDbGwsYmNjoVQqIRaLERkZ6XKJjoERnxOZwPEddwJFUZDL5VAqlSgpKfFLpxmwWOIePnwYCwsLaGpqYv2RuNj6OIPJEFrJJodx0nZHfFLjIvDg+SVBckkPjrMkELhy2csSvHxobNmvW61WCAQCJCYmorCwEPX19di8eTMyMjKg1+vR3t6Ob775Bm1tbRgfH0dfXx/r68al8vEkxRQA3n77bRQXFyMiIgIVFRX45JNP7L5O0zTuv/9+pKWlITIyElu3bkV/f7/H58WgVCrx/vvvr734LPfLNRgMOHr0KLRaLYRCIdLT0/1y/JmZGRw8eBDx8fGor69nu+ZcuUy7i8VigVQqxcjICDZu3Ijs7Oxlf2ZPjnlxXQae/Em51+dHIBC858l9I3j50HGnX3PWas0s0ZWVleGUU05BbW0t4uLiMDY2hs2bN+O6667D7Ows3n77bSgUCrfPg0kxfeCBB9DS0oKqqips27YNMzPOu2EPHjyISy+9FNdeey1aW1uxa9cu7Nq1Cx0dHexzHnvsMTz99NN4/vnncfjwYURHR2Pbtm0wGAxun5ctNTU1i7Hca+lwACzOuDiewtzcHNra2iAWiyESiTA+Pu7zKV+aptHf34/R0VGUlZUtEbfx8XFMTU1h48aNnI/B2OSEhYWhqqrK5ebh3r17sWHDBrc662iaxpH2Plz57hhoUl0QCB6xoywJl2/KwKTKgFcOj6N9UuOT13396uolS3CHDh1CUVHRknC25VhYWMADDzyATz/9FCKRCJ2dndiwYQPeeustrFu3bsXvra+vx8aNG/Hss88CWFw9ysrKwi233OI0xfRnP/sZtFotPvroI/axhoYGVFdX4/nnnwdN00hPT8evf/1r3HHHHQAW3VhSUlKwe/duu6gFT1nzyscWJgW0tbUV69evR0VFBcLCwny2/MVgNBpx7NgxTE9Po6GhwWlV5e2y2/T0NA4dOgSxWIwNGza41bXibpqpxWKBRCLBFx0TIMtaBIJnXN+UhT/tKkFFuhDbSpPx+tW1eP3qaty5NQ87K5O9eu3LXpbgPYl9orCncz6xsbEoKipCRUUF2tracPz4cdx0000uXU+YFFPbEDhXKaaHDh2yez4AbNu2jX3+8PAwZDKZ3XPi4uJQX1/vdjLqcqx5txuPxwNN0zAajWhra4Ner0d9fT2EwsW7B1/uvQCL640SiQQJCQmoqalZNvTN0zA5BtuKqqKiwqN2cHfEh6mmNFYBXuujSIwCgeABO8qS8MvTc5c8XpEuZCuWm3+Ui7s/6EbzcW6Gvb//pB9NeSLWJZuLw4Gto3V6ejquuOIKl9/DJcVUJpM5fT7jbM38/0rP4cqaiw+wsiD4SnyYRNO+vj6sX78e69atW3Ezj8uej22M9nLprCvhSnxmZ2chlUqRmZmJkNAkUHSrR69PIJzs3HpGnsvnpArDsfuKarRPzkNyfB7HVXq80TzldlgjRQPHlXo78fF0EP5EtdaxZc3FZ2hoCP39/Vi/fr3TzXiBQOB2pMJyOGbjuBMs56noqdVqtLa2co7RZo7pTHxomsbQ0BCGhobY/SmZ2hBE7dYEwtpz+xm5HmX22FZD1zRm47Wj43jl+wmXqw18HpCVsNi4RFEUaJr2qvJxFy4ppqmpqSs+n/n/6elpu2U/xk/TG9Z8zyc0NBSbNm1athJhRIBrX4RGo8GhQ4dgMpnQ1NTkdqKpJ5XP+Pg4jhw5guzsbFRXV3MSHgBOW62Z/Z3jx4+jvr6e3Z9KjYvABZWrGwdMIAQrp2VHYGdRNOdVlFRhOH59Zj4+v6UeL/1HJV6/uhpPXFiMHWX2ZsY8HvDAuYWsyDGfZ0/FZ7VSTBsbG+2eDwBffPEF+/zc3FykpqbaPWd+fh6HDx9eMRnVHda88snOzl7xDcH80biY801NTaGjo4NT1II7ez7ObHK8wfGYWq0WLS0tiIiIWGLzI1Mb8O+2KWcvQyAQHLi0NArd3d0wm82Ij49HYmIiRCIRoqKiPJqlSRWGs8LCNCzcekYepONqADxUZQrtqivm2ubpsptGo0FenuslQkc8TTH91a9+hR/96Ef485//jB07duCNN97AsWPH8Le//Q3A4g3xrbfeiocffhiFhYXIzc3Ffffdh/T0dOzatcvj87NlzcXHFUwVYbFY3BYfiqLQ09ODyclJVFVVITnZ8w4W24rL2ZvT1ibHV67atns+MzMzaGtrQ1ZWltO0VGKxQyC4x+1n5OKUuizQNA2dTge5XA65XI7BwUGEhoZCJBIhMTHRpeXNcqQKw5Fa6vwaY7VawePxPBYfrlk+nqaYNjU14fXXX8e9996L3/72tygsLMQHH3yA8vIfZgjvvPNOaLVa3HDDDVCpVDjllFOwZ88erwM713zOx1WaKU3T+Pzzz3Hqqae65efGiAJFUaipqeHsAWc0GrF//36cffbZS944TL5PcnIySkpKfOa60NLSApFIBIvFguHh4RVD5UiCKYHgmks3pOG32wqdfs1qtbKu1AqFAjqdDrGxsawYxcbGeu2Yv7CwgNbWVpx22mkefd95552Hyy+/HDfccINXxw9kAr7y4fF4bm/+z83NQSqVIiUlxWtRYL7XtlOFpmmMjIxgYGAAxcXFyMrK4vz6yzE+Pg6r1WrXbu6MbwbkbnffEAgnK2cVLx8wGRISgsTERDtXarlcDoVCgfHxcQBAQkICu0TH5U6fy3YBwG3PJ9gIePEBVk4zBey7wUpKSpCZmemTYwJgsziYjjmVSoWNGzciPj7e62PYwjjghoWFobGxcUU3bSZSgWgPgbA8tl1n7hAeHo709HSkp6eDpmksLCxALpdjamoKvb29iIyMZIUoPj7eLVHhGqHNpdst2Fhz8XFns2+lysdsNqOtrQ0ajcZlteDpefF4PFitVmg0GrS2tiI8PNwv+T7M/k5ERASSk5Ndvr7n+z3EWZpw8nHr6Z61VtvC4/EgFAohFAqRm5sLi8UCpVIJuVyO3t5emEwmxMXFsWK0XPwBlxkfmqah1WpPyBRTW9ZcfNzBWZopsDhbI5FIEBMTg6amJk6bhSsREhKC2dlZDAwMLLvx7w00TWNwcJDd31EqlW65KnRMeDp5TYSHcHJxfVMWm7PjCwQCAZKSkpCUlASapqHX69kluqGhIQgEAnavSCQSsdcirpUPWXYLEBwrH5qmMT4+jp6eHuTl5SEvL8/noUs0TbNWOZ7a5LiD2WxGe3s7FhYW0NDQgNjYWKjVapfiI1Mb8OcvB3x6LgTCicSWnCinFjq+gsfjISoqClFRUcjKygJFUWzjwujoKDo7O9nGBXeSiZ1Blt0CBNs9H6vViq6uLszOzqK2tpbdLPQljE0ORVEoKyvzufAwy3iRkZF2+zt8Pt+lmwNpsSYQVqZx3epWDHw+nw2FA+zjtOfm5kBRFNra2tiqyNVYhtVqhV6vJ5WPv3E3zdRqtUKr1UIikSAkJARNTU1e95k7w9YmJyoqyucZ6tPT02hvb0d2djYKCwvtfn53jEWDK8WUQFh9ylK4jVf4Cts47eHhYajVagiFQkxPT6Ovrw8RERF2jQuOjigazWK8A9nzCQBCQkKgVqsxODiIjIwMFBUV+XTvhWF8fBzd3d3Iz89Hbm4uvv/+e5+mmQ4MDGBkZGTZZTx3xIex1flAStwNCARHfloUipRY3zYEeQNFUYiIiEBOTg5ycnLYxgWFQoH+/n4YDAbExcWx+0UxMTHQ6XQAcMJXPmvu7eYKiqIwPz+P6elplJWVoaSkxOfCQ1EUOjo60Nvbi9raWnYPyd18HVeYzWa0tLRgamoKDQ0Nyy7juXM8YqtDIDhnR1kytq8T+OXGlCuODQdM40JRUREaGxtRX1+P5ORkzM/Po6WlBWeccQauv/56CAQCjxJMnaFQKHD55ZdDKBQiPj4e1157LVtVLff8W265BUVFRYiMjER2djZ++ctfQq1W2z2P6QS2/d8bb7zh8fmteeWz0rKb0WiEVCqFwWBASkqKyzAlLuj1ekgkEqc2Ob6Ic9BoNGhpaUFUVBQaGxtX7MhzR3zIng+B4JzT14tALagDTnxWWrpnGhcyMzNBURTuuusuvPbaa6BpGhkZGWwM9g033IDcXM+aKC6//HJMTU3hiy++gNlsxtVXX40bbrgBr7/+utPnT05OYnJyEk888QRKS0sxOjqKG2+8EZOTk3jnnXfsnvvyyy9j+/bt7L+5zD2uufgsB5PxIxKJkJCQAL1e7/NjuLLJ8VZ8ZDIZ2tvbsW7duiX7O84gez4EAjd4AKoy4zDcya27zF940u3G5/Oxfft2REdHo6WlBceOHcOXX36Jzz77DAsLCx4dt7u7G3v27MHRo0exYcMGAMAzzzyDc889F0888YTT9Oby8nK8++677L/z8/Pxhz/8Af/xH/8Bi8VitzcVHx/vdSNWQPyVbC/KjIXNsWPHkJeXh8rKSoSGhvo0zZSmaQwPD6OlpQWFhYUoLy932ovPJVCOef2+vj60t7ejoqIC69evd3uY1pX4fN0/R4SHQHDgyoZMpArDObc2+wsucz6MqWhycjIuu+wyvPLKK6isrPToNQ4dOoT4+HhWeABg69at4PP5OHz4sNuvwzRLODZF3HTTTRCLxdi0aRNeeuklTpE3AVX5WCwWtLe3Q61W21nYuLLX4XqMTZs2IS4ubtnnconSZhwXtFqtx2mmriqfsbkF3P+h8zhcAuFkZoNQg6mpKU6OAv7E2whtrshksiVu/swgrLvx13Nzc3jooYeWmJs++OCDOOOMMxAVFYXPP/8cv/jFL6DRaPDLX/7So3MMGPFh3F8jIyOXWNgs53DgKcx8jbN8HGd4uuzG/AzR0dEu93ecsZL4LCws4NNvjxE/NwLBgUurk5CVGI6JiQlYLBZ0dXVBLBYjMTERcXFxaypGXMRHo9Ese9N6991349FHH13x+7u7uz06njPm5+exY8cOlJaW4ne/+53d1+677z72v2tqaqDVavH4448Hp/hMTk6io6MDOTk5KCgoWLJE5YuNf5lMho6ODo9scjxZdmP2d5b7GdxhOfFhXluJBAAqj1+XQDhR4QG45tQ8pArDkZeXh3379iEjIwMLCwvo7OyE1Wq1c6b2Re6WJ3BxtV4py+fXv/41rrrqqhW/Py8vD6mpqZiZmbF73GKxQKFQuNyrWVhYwPbt2xEbG4v333/f5U10fX09HnroIRiNRo/mItdcfGiahkKhWDH0zRvxoSgK/f39GBsb89gmJyQkBCaTacXnMBY8o6OjqKysZEObuOAoPrazQal5JXjl/5ElNwLBlus2Z7Hmocy+Q3JyMrKyFsPjNBoN5HI5O+DJxZnaG7gsA6607Mb4y7misbERKpUKzc3NqKurAwDs27cPFEWhvr5+2e+bn5/Htm3bEB4ejn//+99uDfJLJBIkJCR4PJC/5uLD4/FQUVGx4l6HQCDgtOfD2OQYDAaP918A16JnNpshlUqh0+k4vb4jtuJjsVhYt+6GhgZ0zplJowGB4EBjbgL738xnh7nY83g8xMbGIjY21m7AUy6Xo6enx+tIbXfw9bKbu5SUlGD79u24/vrr8fzzz8NsNuPmm2/GJZdcwna6TUxM4Mwzz8Srr76KTZs2YX5+HmeffTZ0Oh3+8Y9/YH5+HvPziybGSUlJCAkJwYcffojp6Wk0NDQgIiICX3zxBR555BHccccdHp/jmosP4Npih0vlY2uT09jYuKRbwx1c7cG0tLQgJiaG0/7OcsdjbISYCIeGhgaEhYUhhzKQFmsCwQbHvB5H8XHE0Zlap9NBoVCwkdphYWGsECUkJHC6ZjiyVg0HAPDaa6/h5ptvxplnngk+n48f//jHePrpp9mvm81m9Pb2so4KLS0tbCdcQUGB3WsNDw8jJycHoaGheO6553DbbbeBpmkUFBTgySefxPXXX+/x+QWE+LiCER+apt26Mzl+/Dh6enpQUFCAnJwcznczy4meL/Z3nMGIz6FDh5CZmYn169ezHyRiq0Mg2HNFfaZdXo8r8bGFx+MhOjoa0dHRyMrKYiO1GSHS6/V2eT0xMTGcPudc93x8MVAvEomWHSgFgJycHLsW6S1btrhsmd6+fbvdcKk3BI34AIt3ESvdjVitVnR3d2N6etonjtfOohz6+vpw/PjxFfeouEDTNCYmJgAslswZGRl2Xye2OgTCD/AAXL7R/jNCURRr9+IpjpHaer2erYpGRkYQEhLiNK9nJSiKAk3TnCqfE93XDQgQ8XH1ZmEEZyXx0ev1aG1tBY/HW2KTwxXbZTfb/aOGhgafvjmsVis6Ozshl8sBwGlTBLHVIRB+wLbRgMGXA6aRkZHIyMhARkYGKIqCWq2GXC5n83qEQiErREKhcNkUU8C9SswWIj4BhG2ktTPkcjkkEglSUlKc2uRwhal8mP2d2NhYzvtHy2EwGNDS0gI+n4+NGzfi22+/dVqqE1sdAuEHbBsNGPzlbsDn85GQkICEhMVjGo1GNsX0+PHjAGBXFTFdX8yNK6l8nBM04uNs/4WxyRkcHERJSQkyMzN9elym1fr7779Hbm4u8vPzfdoNo1Qq0draiuTkZJSWlrKPO2ty+GZADg4OFgTCCYdjowHDalnrhIeHIz09Henp6aAoCgsLC5DL5ZiYmEB3dzdiYmKQmJiI6OhoTsuARHxWEXd9z2zbrT2xyeECRVEYGxuD2WxGbW2tT/d3gB+aIoqKipCVlQUej8du9jmKj0xtwP0fdhN3AwIBSxsNGNbCWofP5yMuLg5xcXHIy8uDyWRiU0wnJiZA0zTa29vZpFN3tgNOhghtIEDExx1sLXY8tcnxFGZ/R6fTgc/n+1R4KIpCT08PpqamljRFMHdJjuJD9nsIhEWcNRowBIKpaFhYGFJTU5GamgqlUomOjg7Exsa6PeRK0zS0Wu0Jn2IKBJH4MMtuTJtzdna2227RnjA/P4/W1lbExsaipqYGBw8edLvF2xVGoxESiQQWi2XZpghnZqYdE/NeH5tAOBFg3KudEQjiYwtFUQgNDV2SYmo75JqQkMDuFzHXA51Oh6iotY0CXw0C4i/lzoWdz+djfHwcHR0dqKysRFFRkc+FZ3JyEocPH0ZmZiZqamrYjUMuduGOzM/P49ChQwgPD0d9ff2y5bfjYKtMbcCfvxzw+vgEQrCzUtUDBKb4OEsxLS4uRlNTEzZu3IiEhATI5XIcOXIEv/jFL3DNNddgfn7eJz+Hp0mmwOKsj2NK6Y033mj3nLGxMezYsQNRUVFITk7Gb37zG04ONEFR+ZhMJmi1WvB4PJ+3OQOLb5K+vj6Mj4/bze/Yzhd582aYmppCR0cH8vLy2Iju5XAUH7LkRiAs4qy92pZAE5+Vrhu2Q67Z2dmwWq3QaDR4//332ZWRU045Bdu3b8dPfvIT5OXleXx8T5NMGa6//no8+OCD7L9tqzCr1YodO3YgNTUVBw8exNTUFK644gqEhobikUce8ej8Al58VCoVJBIJ+Hw+srOzfS48JpMJEokEJpMJjY2Ndht9zBvHarVyss/hMpTqKD45oijwANJsQDjpEVvmMDa2OAzqzIeNi5uAP/HEWickJATnnXcempqa8Pbbb+PIkSM4dOgQ9uzZg6ysLI/Fh0uSKUNUVNSyBsyff/45urq68OWXXyIlJQXV1dV46KGHcNddd+F3v/udR/vvgXOb4ITjx4/j6NGjWLduHRITE32y/GWLWq3GwYMHERoaioaGhiUdJnw+32kDgDuYzWa0tLSwJnzuNi24E6VNIJxs8HlASVYSlEoljh49ikOHDqG3txezs7Pskk8gVj5crHUAoKysDP/1X/+Ff/3rX7j00ks9PrY3SaavvfYaxGIxysvLcc8997DnxLxuRUWFnXv/tm3bMD8/j87OTo/OMSAqH8c7GMYmZ2Zmhu0I6+rq8lmaKbC4v9PZ2elyKYyLqalGo0FLSwunUDlny26k6iGc7FxRn4maohwAsPNhGxgYgMFgQHx8PHg8Hvh8vs8ahLyFq6loZGSk1xUc1yTTyy67DOvWrUN6ejra2tpw1113obe3F++99x77uo6xMcy/3U1IZc/Ho2f7EWbOxdYmp7Gxkd2Y91WU9qRKh28lfeBp57BlU7XLbAxPxWdmZgZtbW3Iysri1I3nGGBHnA0IJzuOjQaOPmyMO/Xx48eh1+tx6NAhn7tTc4HLMqBGo2GHU53h7yRT28jsiooKpKWl4cwzz8Tg4CDy8/M5v64zAkZ8gMXMcKlUitTUVJSUlNiV0AKBAEaj0avXf+PIKH73cT9oLJbxD6aacLGLXCZ3l8FomsbQ0BCGhoZQXl7O2ZXW8XjE2YBwsrNSezWwuEcRFRUFg8EAq9UKsVi8pCpixMofmT3L4esgOWB1kkxtYYLnBgYGkJ+fj9TUVBw5csTuOdPT0wCce1KuRECID03TGBwcXNEmx9so7YM9E3jg43723xQN3PfvbpxakIjUuOXT+tw5rsViQUdHB1QqFerr6yEUCjmfp634EGcDAgE4u0Ts1vOYSsNZVSSXyzE0NOSXzJ7lsFqtHqd7MuKznED6O8nUEYlEAgDszXRjYyP+8Ic/YGZmhl3W++KLLyAUCu0swtwhIMQHWHSlXskmx5tltxf2duLPX09isYD/ARrAnz7rw93b1i8rQI7LYM7Ou6WlBQKBAI2NjR6/2Zwdj7FiP9gxQJbbCCc9BrN7DTjOXO+ZqigzM3PZvSJ/VUVrGSTHJcl0cHAQr7/+Os4991wkJiaira0Nt912G0477TRUVlYCAM4++2yUlpbi5z//OR577DHIZDLce++9uOmmm4IvRhtwP0rb08qHoih819qFP38tAw3nb6pPO2ewp3MGvzmrAGUZQkSFhkBntiJHFIXUuAinjgMytQEjCh3i+SZMDHQiLS0NxcXFPum04fP5sFgskEqlODog9/r1CIRgZjkTUWe46nZzVhUx7tT+qIq47vn4apzE0yTTsLAwfPnll3jqqaeg1WqRlZWFH//4x7j33nvZ7wkJCcFHH32E//qv/2JHU6688kq7uSB3CQjxcQdPl90YK5veaYPLZSsawGNf2LsI8HnAHVsLINBQmA/VYMyoQI4oCt8MyHH/h92gaIAHGrefmoozPSw3VzwXmsbx48dh4EXgg2FS9hBObpYzEXWGp63WTFXkmGTqq6qIy56PL611PE0yzcrKwldffeXyddetW4dPPvnE6/MLKvFxd9lNrVajtbUV8fHx2H5KGZ5o/t7jfROKthUkLYCxJV1nNHj4y7fTuGBjIYDFtmimYuKCSqXC7OwsoqOjEZG6HhTdyul1CIQTAVd2Oo54M+fjj6qI67LbyRCnAASQ+LiTZupO5TM+Po7u7m4UFBQgJycHPB4PVzdl46WDY16fo7P9F4oG/vrVEN5snvyhi+78Elxct/ihYZboXInSxMQEurq6EBcXB6FQiO+mFrw+XwIhmHHV5eaIL4dMfVEVEfFZmYARH1e4WnazjSqoqamBWPxDh8yVDdnYfWjMb5v3bzRP/nAe/9dFV5QSg087p/HywTGnosRga8FTU1MDuVyO6QUTMRMlnNR4WvUA/nM44FoVEfFZmaATH2fTy7ZRBY2NjUvWTFPjIvDrrQV4/IvVuaDTAC5+4ajdYxQN3P+hfWs301ig0+nYzTulUomJeRPpciOc1LgyEXXGanm7uVsVcZ3zEYlEfjrzwCJgxMfVsputw7TteqtKpUJraytEIhHKysqWXYstz+A+e+MrKBr4tHMa55SlIFZgRUtLCyIjI9HQ0MBa8PD5fKRG8YmZKOGkpjE3wePvWQtvt5WqIrPZjPb2diQlJbm9V0QqnwDEtpRl/tvZ/s5yBIo79J8+68ejn/fjjAzgsrpUZOTlo3l8gd0T4vP5oGhiLEo4efGkvdqWQDAWtZ0r2r9/P/Ly8qDRaNzeKzpZUkyBIBIfxmHaarWCoih0d3dDJpMtiaJejtS4CJ81HngLTQN7x4G94zLwIGP3hK5qzMaZWXxMzlvWXCQJhLXCk/ZqWwJBfBiY2UCxWMwOdS63V5SYmIiEhASEhIT4rNVaoVDglltuwYcffsjO+PzP//zPslXVyMgIcnNznX7trbfewsUXXwzA+QrVP//5T1xyySUen2PAiI87PfQhISHQ6/Voa2uD1Wp1ur+zEv5uPOACcyoUDbx0cAwvA6hMDpxMEgJhdaFRGSHHyAgfYrF4RasZRwJRfGz3oJbbK+rv78f777+Po0ePYnx8HGq12mtnbk+D5LKysjA1NWX32N/+9jc8/vjjOOecc+wef/nll7F9+3b23/Hx8ZzOMWDExx34fD4kEgmbNeHp5uJqNx5wgQYgneHuYUcgBDOX16WiNCcGcrkco6OjEAgEdtXBSnsmgSQ+TGfucufjuFckEokgEonwl7/8Bffccw+efvppnHPOObj00ktx2mmneXRsLkFyISEhS4xB33//ffz0pz9dUi3Fx8d7bCLqjMD4S7nB8ePHYTKZkJKSgsrKSs5dLYHQeEAgEJay2F6djuTkZJSVlWHz5s0oKSlBSEgIBgcH8c0336C1tRVjY2PQ6XRLwiUDTXyYrQJ3KCoqwl133YWEhAR89NFHeP755xEWFgapVOrxsb0JkmNobm6GRCLBtddeu+RrN910E8RiMTZt2oSXXnqJc8hnwFQ+y/2RbPd3oqKikJSU5FU5GiiNBwQCwZ4r6zOQHh8FiqLYyiEmJgZCoRD5+fkwGAyQy+WsQ3V4eDhbPQiFQtA0HTDiw7XtW6fTISEhARs2bLBb2vIErkFytrz44osoKSlBU1OT3eMPPvggzjjjDERFReHzzz/HL37xC2g0Gvzyl7/0+DwDRnycYTAYIJFIQFEUmpqa0NbW5nWgXCA1HhAIhB84pzwFYWFhrKs7RVHsf1ssFggEAqSmpiI9PR0URUGtVkMul6OnpwdmsxnADxdeJoRyreAyYAqs3O3m7yA5Br1ej9dffx333Xffkq/ZPlZTUwOtVovHH3/8xBIfpVIJiUSCxMRElJWVISQkhJOztTOuqM9inQcIBEJgoP+/6ASmemEu3owIMf9jrgFCoRDx8fEoKCjA/Pw8WltbMTc3h6GhIURFRbFVUVxc3KpXRFwGTE0mE8xm87Lis1pBcu+88w50Oh2uuOIKl8+tr6/HQw89BKPRGJyRCoD9stvx48fR09ODwsJCrFu3jv2at4FywOKbYnasHxfmAe8NefVSBALBR/B5QLbIebXC5/PZCzlTCTFuJ0yFxDQiVFVVgaIotpOss7MTVqsVIpGIFSNvM7fcgau1DoBl26FXK0juxRdfxAUXXODWsSQSCRISEjj9TgNGfIDFN1ZXVxdmZmaczu94EygHLC7jtbYuOkWf01CO94Y6vDpfAoHgG65syEKq0LUbvLOqyGw2Y2RkBDExMWyLc3x8PEQiEdavXw+tVgu5XI7JyUn09vYiJibGbq/IH7HaXMRHo9EAgNdzPlyC5BgGBgbw9ddfO41M+PDDDzE9PY2GhgZERETgiy++wCOPPII77riD03kGjPhYLBYcOXIEFEWhsbHR6ZqtN5UPs4wnFotRWlqKWY2ZNB4QCAEAD8DP6zM5f393dzf0ej1qamoQGhrKDqIzQhQREYGsrCxkZ2fDbDazVZFUKgWPx7OrihibK2/h0nDApJj6YonQ0yA5hpdeegmZmZk4++yzl7xmaGgonnvuOdx2222gaRoFBQV48skncf3113M6Rx7NtU/Ox9A0jaGhIaSlpS37R+vr64PZbEZZWZlHr83Y8Ngu473dPIF7/+395hyBQPCOXeWJ+MOFFZzC2tra2mAymVBbW7tEOJj9IWapjrnU8Xg88Pl80DQNjUbDdtBptVoIhUJWiGJiYjhXRWNjY1Cr1aioqHD7e44ePYpLL70UMpnML9VYoBEwlQ+Px0NWVtaKPeMhISEwGAxuv6ZtzILtMp5MbcD9HxLhIRACAZFFjq+++gpisRhisditCsRqtUIikcBqtToVHmD5vSLbpoWoqCjExMQgNzcXZrOZFaLR0VF2EFQsFnscq81l2c2XKabBQMCID7AoQK7Ex909H5PJBIlEApPJtMSGZ0ShCyiLHQLhZIUH4LKzGxBJGzA3N4fh4WF0dHQgLi4OYrEYSUlJSyx2LBYLJBIJaJpGbW2tW6LgbK/ItiqyWCzg8XhISkpCSkoKaJrG/Pw85HI5BgcHodfrPYrV5rrn44mdULATUOLjCndbrZm2S6FQ6PTNmSOKWhKJTSAQVp+rGrOQHh8JIBIJCQkoLCyEXq/H3Nwc2zYdFhbGVkVCoRBtbW3g8Xiora3l7HTiWBU5a+W2HXA1Go12A67OTEFt4brnc7LEKQBBJj7uNBzIZDK0t7cjLy8PeXl5Tu8iUuMi8OD5Jbj/w24iQATCGrFco0FkZCSysrJYA06lUom5uTn09PTAYDAgNDQUubm5MJlMPhkmdbY85zjgGhISgpSUFKSlpdkNuPb19cFkMiEhIYEVo8jIyCW5Y+7ANBycLASU+LgTKLfcshtN0xgYGMDo6CiqqqqW2Es4cnFdBk4tSETrcRVuf6eDiBCBsMpc1ei6vTokJARisRhxcXFQKpWIj4+HWCzG7Ows+vv7WcutxMRExMfHe90pttzyHCNIzgZcGdufmZkZ9Pf3IzIyEjRNIz4+3iO/OSI+AcxylQ8TR63VatHQ0OB26ZoaF4Fz4lIxoTIEtNM1gXCi4Ul7tclkQnNzM6KiolBRUQE+n882CCgUCszOzqK9vR0URbENAmKxGGFhYV6f50oDrkwrd2hoKNLS0pCRkcFGJfT392NmZgYzMzNuD7iSZbcAxtmej1arZeOoGxsbOfXpE6drAmF1ubg2za2hUqPRiObmZsTExKC8vNyuiggNDUVKSopdg8Dc3BzGxsbQ2dnJNi2IxWLExsZ6vZHvblWUkJCAiIgIpKSkIC4uzm7ANTo6mhVIxwFXjUZDxCdQcax8ZmdnIZVKkZWVhfXr13N+cxGnawJhdWnITXD5HIPBgObmZsTFxaG0tHTF5Ssej4e4uDjExcWxDQJM08LIyAi7fJeUlASRSOTxfowzlquKtFottFotQkNDER4ejszMTGRlZS0ZcAXAzhOFhYVBp9P5ZNntD3/4Az7++GNIJBKEhYVBpVK5/B6apvHAAw/ghRdegEqlwubNm/HXv/4VhYWF7HM8TUd1RWD4j/8f7uz5MO2Rw8PDkEgkKC0tRVFRkVd3NYzTNYFA8D88ANVZcSs+R6/X49ixY4iPj0dZWZnHeznh4eHIyMhAVVUVtmzZgoqKCggEAvT39+PAgQNobm7G6Ogo66fmLXw+n92Tbm9vR3p6OsRiMTvMyhiNJiYmori4GJs3b0ZVVRUiIyPx6aefoqSkBG+99RZaW1vR0tLCLulxwWQy4eKLL8Z//dd/uf09jz32GJ5++mk8//zzOHz4MKKjo7Ft2za7ucrLL78cnZ2d+OKLL/DRRx/h66+/xg033MD5PAPG4QBY7I1faY7HbDZj7969SE1NhUqlQk1NDeLiVn4Tu4tMbcCWJ78l1Q+B4GeubszCb84qWPbrjPCIxWIUFxf7fO5Fp9OxVZFCoUBERASSkpLYYVKuTQs6nQ7Nzc1ITk62W4lxHHC1veQy1dPx48dx6aWXAgBGR0cRHR2NK6+8En/60584/5y7d+/Grbfe6rLyoWka6enp+PWvf836tKnVaqSkpGD37t245JJL0N3djdLSUrt01D179uDcc8/F+Pi403RUVwRU5eMKk8kEYPHN2djY6DPhAYD4cGBbTlCtQhIIQYerRgOtVoujR48iKSnJL8IDLLoaZGdno7a2Flu2bMH69ethtVrR2dmJAwcOQCKRYHx83CM3Fb1e71R4gB+qorCwMISFhSE8PBwCgYCtiiwWC9LS0hAZGYkrrrgCc3Nz+Oc//4na2lqf/+zOGB4ehkwmw9atW9nH4uLiUF9fj0OHDgHwTTqqIwF1tV3pjaZUKllH6oqKCp/aoqvVarS0tODC0gR8NjJHqh8CwU+s1F6t0WjQ3NyMtLQ0FBYWrsqkv0AgQHJyMpKTk1mvt9nZWUxOTqKnpwcxMTFs00JcXJzTc2IqtaSkJJd7z0xV5TjgykSEn3HGGQgLC8OWLVv88vM6g0k3TUlJsXs8JSWF/Zov0lEdCYrKZ2xsDMeOHUNBQQFCQ0O9Wg91ZHJyEkeOHEFubi5+tKmK7P0QCH5ke6nzjBhGeDIyMlZNeBzh8XiIjY1FXl4eNm3ahNNOOw3r1q2DXq9Ha2srvvrqK3R0dEAmk7HJqUxThFgs5rT3zOfzWUPRp59+Gn/84x+dPu/uu+8Gj8db8X89PT1e/w5Wk4CqfByhKArd3d2Ynp5GXV0dRCIRhoaGfJJmStM0+vv7MTY2hurqajY46cqGbJJySiD4CSat1JaFhQU0NzcjOzsbeXl5a3BWzgkLC0NaWpqdq4Gt/1xsbCx0Oh1EIhHnpqejR4/ixz/+MR5++GHceOONy76GuymmXGDSTaenp5GWlsY+Pj09jerqavY53qSjOiOgxMf2F280GlnXWtt8H1+kma40lJoaF4E7ziogQ6cEgo9xllbKLHnn5OQgNzd3jc7MNXw+HwkJCaz/nEqlgkQigUAgwNzcHL777jt2eU4kErnl69ba2opdu3bh3nvvxS233LKieLmbYsqF3NxcpKamYu/evazYzM/P4/Dhw2zHnLfpqM4IKPFhUKvVaG1tRXx8PCoqKuz+kN6mmep0OrS0tCA8PHzZodTrTsnBmEKHN5snOR+HQCDYc/uZeXb7PSqVCq2trcjLy8O6devW8Mw8w2g0orOzE0lJSSgtLQVFUXb+cyaTCSKRiBUjZ/5z7e3tuOCCC3DHHXfg17/+tU+XGcfGxqBQKDA2NsZGTwBAQUEBe6NdXFyMP/7xj7jwwgvB4/Fw66234uGHH0ZhYSFyc3Nx3333IT09Hbt27QLgXjqqpwSc+ExOTqKzsxP5+fnIzc1d8kfxpvKRy+WQSCRIT09HUVHRii2V2aKTJ1eDQPA3P61NwzVNPwgM00BUWFiIrKysNTwzz2AcF5jBVx6Pxw6wMvs+Wq0Wc3NzmJ6eRm9vL+s/Nz8/j/LycgwODuL888/HzTffjN/+9rc+39+6//778corr7D/rqmpAQDs37+fbWTo7e2FWq1mn3PnnXdCq9XihhtugEqlwimnnII9e/YgIuKHmwVX6aieElBzPnq9Hl999RXKy8uXLTGbm5uRlJSE7GzPGgPGxsbQ29uLkpISZGau7CklUxtw+l++JWajBIIP4AHYe2sjW/UoFApIJBKsX7/e5WcxkDCZTDh27BiEQiHKysrcEg1b/7nLLrsMk5OToCgKW7duxUsvveTSAPlEJqC63SIjI3HaaaetuLbpaeVDURS6urowMDCADRs2uPVmJ2FzBILvuOGUbFZ45ubmIJFIUFxcHJTCExsb67bwAD/4z5WXl+Odd95BVFQUKisrIZPJkJaWhoaGBnR2dvr57AOTgFt2EwgEPk8zNZvNdk0LriBhcwSC72jMEwFY9GJsa2tDaWmpXVdVoMO4asfExHgkPLaMjIxg586duOSSS/D000+Dz+dDJpPh008/5bxnEuwEVOXjDu6mmWo0Gnz//fcIDQ1FfX29R6FTTNgc/+RIsyUQ/AbT4TYzM4O2tjaUl5cHpfBERUUtcdV2l4mJCezYsQPbt29nhQdYbF+++uqrkZDg2mT1RCTgKh9XhISEsANey8G80detW4eCggJOdyq2YXO3vt3B9XQJhJOa28/MA3QqtHd2oqKiIqj2OMxmM1paWuxyhDxlamoK5557LrZs2YL/7//7/7wOuzuRCDjx4fF4LpfdlvNcomkaw8PDGBwcREVFBefhJwYmbK5/UoHnviNt1wSCJ/y0Ng3n5Iahq6sLVVVVEIvFa31KbmM2m9Hc3IyIiAjOwjM9PY3zzjsPmzZtwgsvvODW7M/JRNDJ8HJ7PlarFe3t7RgbG8OmTZu8Fh5bzs0Lw1np3rsqEAgnCzwAu9ZHoLu7OyiFh5kFrKys5CQ8c3NzOP/881FeXo7du3f7JD/oRCPofiPO9nwMBgNaW1vB4/HQ2NjoM9NRmqYxMDCAkZERXJDLQ3xKGt5unfLJaxMIJzI/q0yAYnwI1dXVEIlEa306bmM2m9Ha2oqwsDBUVVVxEh6lUomdO3eioKAAr732Gqd05ZOBgKt83A2UY1Cr1Th06BCio6OxadMmnwmPxWKBRCLB5OQkqqqqQFEUflYRB9KDQCC4JplSoLa2NqiEx2KxoLW1FQKBgHPFo1arsXPnTqSnp+PNN99EWFiYH870xCDoKh/bZbepqSl0dHSgoKAAOTk5PpsUNhgMaGlpQUhICBoaGsDj8ZCZmYnpkV7sygHeH/HJYQiEExIeaKTG8DE1NQWz2ey219laYrFY0NLSAoFAgKqqKk7nu7CwgAsvvBAikQjvvvuuT2NfTkQCyuEAWHwTrNRKLZfL2ZjasbExVFVV+dRwjzE6FIvFKCkpAbA4qMoEP6nVajz55QDe7db47JgEwonETZvTcUm1GLOzs5idnYXJZEJiYiLEYjGSkpIC7qLMVDx8Ph/V1dWchEer1eKiiy6CQCDARx99hOjoaD+c6YlFwImPqyhthUKBo0ePIjIyErW1tXaO1N5iW0llZWWxXXdMXoYtT+0dxN++G/PZsQmEE4HtxQl48qfV7L9pmoZWq2WFaH5+HrGxsWxsdWxs7Jpk9zBYrVa0tLR4JTx6vR4/+clPYLFY8MknnyA2NtYPZ3riEVTio9PpcOzYMeh0OjbxzxfQNI3BwUEMDw+jsrISiYmJrPCstO77P/sG8b/fEgEiEBj22Xi4OcNkMmFubg6zs7OQy+UQCASsEK328pzVamXTkWtqajgd22Aw4JJLLsH8/Dw+++wzxMXF+fo0T1iCZs9HoVCgtbUVycnJ0Ol0PusgYVq0VSoV6uvrER0dDavVCj6f7/KO7Fdn5CM2QoA/fzm0quFzMWF8ZMaFIyJMAK3RAp3ZCgGfj8ToUFhpQGcyg6J5SI4JQ0QoH7J5E3QmK6LCQpASGwYeD1DqLKABJEQKEBkaAoPFCplaD5XGAFEkH0kJcVDqLexrxUUIQNFYcjyKBlQ6MzRGC0xWCvNG36XMEoKLq1eIyGYICwtDeno60tPT2SiC2dlZNopgtZbnmKgBmqZRW1vLSXiMRiN+/vOfQ6FQ4IsvviDC4yEBV/lQFLXEweD48ePo6elBcXExG3q0detWr3vnbVu0q6urIRAI2P0dT5YCZPMGSI6r8WX3ND7pkjt9TkI4kBFJw2DlYYHiQxQVhpjIMOhNVswbrRBHhyJVGA6FzgydyYocUSTio8Jgslih0FmQFR+BsgwhqrPiXH7AubCwsIDW1lYkJiaipKSE8yQ287sYU+hwXGmAzmgBjwfQ4GF63gDZvBFhAj4iQ/nggQczRWF63khEK8hxdK72lOWW5xgh8uXyHCM8FEWhpqaG03XEbDbjiiuuwMjICPbt24fExESfnNvJREBXPhRFoaenB1NTU2yMNkUtXqSsVqtX4jM/P4+WlhaIRCKUlJSAx+NxEh4ASBVGYHO2GVFyFc7PFiFcnIUc8WIe0JhCj2xRJFKFEbBarVAoFJiZmcHs7CwAI5KSkpCcnLymHUFyuZy1I3KWoeQJqcIIbC/z/AIkmzfgQO8cOqcWoDdZoDNTmFkwQGukECrgATSNcaURBmtA3SsR/o9fb83z6qaIx+MhJiYGMTExyM3NtVueGx0d9dnynNVqhVQqhdVqRW1tLadriMViwbXXXovBwUEiPF4QsJWPyWSCVCqF0WhEbW0toqJ+CHf77LPPcMopp3DuKJmenkZbWxvy8vKQk5PDCpqzxgJ3mJ2dRXt7O3Jzc91u+aZpGiqVCjMzM5iZmYHZbGbv8sRi8aoNpk1OTqK7uxslJSVB4a7bPqHGxx3TmJ03QqvTYUGjRUhENJRGGlaKglJngdpA3ChWk/PKk/HYRWV+e33b5TlvuucoioJUKoXZbOYsPFarFf/5n/+J1tZW7N+/36dOKicbASk+SqUSLS0tiImJQWVl5ZI3yd69e7Fx40YIhUKPXpumaQwNDWFoaAgVFRUQi8VuNRas9HpjY2MYHBxEWVkZUlJSPH4N5nU0Gg0rRFqtFiKRCMnJyX5b+2Z88EZHR9kmi2CBpmn09/djcnIStbW1S94HzNJf5+Q8mkdVWDBZESXgQ6G3QKkzQWcOqLd80OOqycCXcF2eY4THZDKhtraW082d1WrFLbfcgu+++w4HDhxARkaGL36kk5aAEx+VSoXvvvtuRUfqAwcOoKqqyiMrcqvVis7OTigUCtTU1CAmJsbtxgJnMEuCs7OzqK6u9ulmo06nY5fm1Go1hEIhkpOTkZycbFcBcoWiKHR3d0Mul6OmpiaoWkOZcECVSoWamhpO1a9s3oB/S6ZwaFgJg4VCVCgfs1ojdEYKkaF8HFcaYCJbUG5xx9Y8u3js1cad7jmKotDW1sauonARHoqicNttt2Hv3r3Yv38/1q1bu5/5RCHgxMdqtUImk61oRPjNN9+guLjY7eFSo9GI1tZW0DTNbjBy3d8BFjcb29raYDKZUF1d7VFWkKcYjUbMzs5iZmYGCoUC0dHR7D4Rl01Yi8XCfhBramrsMtoDHWa9nrmI+LMbqn1CjQP9cii1JvTINFgwmCHg8yDXmqHSW2AJqE/N2nD5xnT89zlFa30aLM6W50QiEYxGIyiKwsaNGzkLz1133YUPP/wQBw4cQF5enh/O/uQj4MSHpmmYTKYVn3Pw4EHk5eW5td66sLCA5uZmxMfHsymE3giPTqeDRCJBZGQkKioqVtWt1mKxYG5uDjMzM5ibm0NoaCi7NJeQkODy5zEYDJBIJAgNDUVVVVVQOe0yqbR8Ph9VVVVrbtbYPqHGW82TOK7UQ2MwY1ptAEVT0BgpmAPPMtHn/KggAX+9rHqtT2NZaJrGwsICOjo6oNfrQVEUhEKhx91zFEXhvvvuw1tvvYX9+/dj/fr1fj/3r7/+Go8//jiam5sxNTWF999/H7t27Vrxew4cOIDbb78dnZ2dyMrKwr333ourrrrK7+fqDQF39XHnDeFumunMzAykUilyc3ORm5sLiqJA0zRn4VGpVJBIJEhLS8P69etXfTJbIBAgNTUVqampoCgKcrmcjSYGsGLnnEajQWtrK9vdF0yhVnq9Hq2trYiOjkZ5eXlA+IRVZMShImPpUqvFYsF33cfxZZcM02oDRucBjQUIDwFovgBzOguCvWEv0CoeZ9A0jZGREfB4PJx66qkA4HH3HE3TePjhh/HPf/5z1YQHWLTqqaqqwjXXXIOLLrrI5fOHh4exY8cO3HjjjXjttdewd+9eXHfddUhLS8O2bdtW4Yy5EXCVD7C41LQSzc3NSEpKQnZ2ttOvM2+8gYEBlJeXIykpaUWrHHeYmppCV1cX1q9fj6ysLI+/35/Yds7ZdgMlJydDLBZjYWEBUqkU2dnZyMvLW1M7E0/RaDRoaWlBUlISiouLg+rcdTodmpub2YBEk8kEsVgMOWKwd9iA3hkt1HoLLBQFvcmCeWPAfRSXEAzCQ1EUOjo6oNVqUVdXt8QJZaXuucTERERGRoKmaTz66KP461//in379qGiomJNfhYej+ey8rnrrrvw8ccfo6Pjh8TlSy65BCqVCnv27FmFs+RGwFU+gHtppstVPhRFobOzE3Nzc9i4cSNiYmK8WmZjOuQYE9NADMXi8XhISEhAQkIC1q9fz3bOjYyMoLOzEzRNIy0tDZmZmUF18VYqlZBIJEEpmjqdbskcmUajwezsLAyzszg9ZgG7MuKQlJSOpKQkREdHLzZCSKfQMqaGxmiBQmuG1miBymCBOQAaIH5UkBDwwkPTNDo7O6HRaLBhwwanFlx8Ph+JiYlITExEUVER2z03OTmJe++9F21tbUhMTER7ezsOHDiwZsLjLocOHcLWrVvtHtu2bRtuvfXWtTkhNwlI8XGFQCBw6v9mMpnQ2toKq9WKhoYGhIaGeiU8TIecWq1mhSzQ4fF4iI2NRUxMDHg8HkZGRpCamgqtVotvvvmG7ZxjLniByszMDDo6OrB+/XpkZmau9el4BFOtJScno6ioiH3vxcbGIjY2Fnl5eTAYDOyd98DAAKKiopCUlISfViTh+lOWzooxe0zdsnmo9VZYrBRUOjNWyxgiGCoeRngWFhacVjzOcBxuzcjIwO233449e/YgLCwMF1xwAc477zxcfvnl7PJdoCGTyZaMeaSkpGB+fh56vd6vDVHeEJTi46zy0Wg0aG5uhlAoRHl5udeNBUajEVKpFABQX18fVKFQTBs4U/0xrdRM55ztBY9p4V5rd2FbJiYm0NPTg/Lycs6zU2uFWq1Ga2srsrKyVqzWIiIikJWVhaysLFgsFnb/jrH2T0pKQlJSErsfsdweEzN0OzCtwbTGCKOZxpTaCF+O2a51O7U70DSNrq4uqNVqbNiwgVMnJE3T+Oijj/D111/jq6++Ql1dHb7++mt8+OGHaGlpCVjxCVYCUnzcWXaz9X+bnZ1l9zTy8/O9bixgNufj4+NRWloaEBvc7mLbSr1p0ya7Vurw8HBkZmYiMzPTrnPu2LFjCA0NZRsW4uPj16QhgdmrGxkZQU1NTVClYAKL5rdSqRR5eXkezYEIBAKkpKQgJSUFFEVBpVJhdnYWvb29MBqNdvt3jjdBrkSpf1qDMaUBcq0RhuWTSpZQlR6DKxuz/eYl6EsY4VGpVKirq+MsPLt378YDDzyAjz76CE1NTQCAs846C2eddZavT9mnpKamYnp62u6x6elpCIXCgK16gAAVH1eEhIRAr9eDpmmMjo6iv78fpaWlbBcYwL2xYG5uDu3t7UG5z8DMM4WGhmLDhg0rtiM7ds4xnnPt7e2gaZq9805MTFwV8aVpGr29vZiensaGDRuCavAV+MFiqaioyKvJdz6fD5FIBJFIxO7fzc7O4vjx4+jq6kJcXBz7t1lp2dSZKDHDtS3H1TBbKejNFMIFPGQlREA1N4vIiDBkpKXg9PVip4IWiNA0je7ubiiVSmzYsIHT3BpN03jttddw991341//+hdOO+00P5yp/2hsbMQnn3xi99gXX3yBxsbGNToj9wjIbjez2cyKiDNGRkYgl8sRHh6OmZkZdkqfoijweDzOd+3Hjx9HX18fSktLkZaWxvX01wSmWktISEBpaSnn3wHTOccMtjp2zvljvobpTpqfn0ddXV1A3605QyaTobOzE2VlZX71+rLdJ1IoFOw+UVJSEuLi4jjdKBkMBjQ3NyMuLo6dgwsWaJpGT08P5HK5V8Lz9ttv4+abb8Y777yD7du3++FMPUOj0WBgYADAYs7Qk08+idNPPx0ikQjZ2dm45557MDExgVdffRXAYqt1eXk5brrpJlxzzTXYt28ffvnLX+Ljjz8mrdae4ipKm2mjjoyMRE1NDcLCwrzuaOvt7YVMJkN1dTXi4+O9OPvVh1nu8XW15sxzLiEhgW1Y8IU7gsVigVQqhcViYf+WwcT4+Dj6+vpQWVm5qp2QtvtEs7OzTveJXKHX69Hc3MzesASr8Hhzw/L+++/jhhtuwJtvvonzzjvPx2fJjQMHDuD0009f8viVV16J3bt346qrrsLIyAgOHDhg9z233XYburq6kJmZifvuuy/gh0yDTnw0Gg2OHDkCiqLwox/9yOvGAovFgvb2duj1etTU1ATdXTczf1RcXOx3o0O9Xs8KEeM5x+wTcemcM5lMaGlpCUrHBWDxJmh4eBjV1dUe+Qz6Gtt9otnZWZf7RMAPM0hisTjo5qeYm8XZ2Vls2LCB82f2o48+wtVXX41//OMfuPDCC318lgRXBJX4zM3NQSKRIDExERqNBo2NjaBpmvP+jl6vh0QiQVhYGCorK9fcssUTmM15Jvp7teePTCYTO9Qql8s97pxj5mCY5Z5gclxgYtfHx8edumqvJUy1ygjRwsLCkn0irVaL5uZmpKSkrIlThzfQNI2+vj7MzMx4JTx79uzBz3/+c7z00kv42c9+5uOzJLhDQIqP1WpdMsczNjaG3t5elJSUIDo6GkePHkVqaiqSk5ORmJjo8cVLrVZDIpGwsxjBdPGjKAq9vb3sftdaX/ycec6t1Dm3sLCAlpYWpKSk2M3BBAPMXffMzAxqa2sDfvbLYDCwfxuFQoGIiAgYjUYkJycHpej39/dDJpNhw4YNnB3e9+3bh0suuQTPP/88Lr/88qB6/51IBLz4MDMrzH6MUChcsilusVjYi5073VnT09Po7OxEfn4+srOzg+rNZ7Va0dbWFrDLhLadc7Ozs0s659RqNaRSKXJyctwO3gsUbOMcgrExQqVSoaWlBZGRkTAYDODz+RCLxWuepOsONE1jYGAAU1NTXgnP119/jYsvvhj/8z//g6uvvjqo3n8nGgEtPmazGRKJhLXQDwsLW7LMRtM05ufnMTMzg+npadY/i1nvtt1HYALURkZGUFFR4XYkQ6BgNBohkUgQEhISEM7OrqBpGmq1mt0nMhgMoGka6enpWL9+fcCfvy0URaG9vZ31C/NnnIM/YGLjmaaU5faJmBuFQGr8YIRncnISGzZs4OzMcfDgQVx00UV47LHH8J//+Z9EeNaYgBQf5oPR0tKCqKgoVFZWsoOnK+3v2HZnTU9PQ6/XQyQSISUlBYmJiejv72fD5IJtjkSr1aKlpYWNhgim5RJgcdm0v78fycnJ0Gq10Gg0Pu+c8xdWqxUSiSRoO/LUajVaWlrYmHdHmHRQplp1tk+0VjD7axMTE14Jz9GjR7Fz50489NBDuPnmm4nwBAABKT5zc3M4cuQIMjIyUFhYCJqmOXW0MR8omUwGjUaDkJAQ5OXlIT09PaguIIzBZlZWFvLz84Pqg2NrzFpTU8O2sfu6c85fmM1m1vKmuro66DryVCoVWltb2SVmd3DcJ/LFPBFXmMaOuro6zvtrra2tOO+883Dvvffi9ttvD6rPz4lMQIqPVqvF9PS0TxwLtFotWltbERUVhYSEBDb3PT4+nu3OCuS7bmaAsaioKOgMNpnp87m5uRU3500mk11aa2RkJFsRCYXCNbtYGI1GtLS0ICIiApWVlQG9J+IMpVKJ1tZWFBYWco4BsZ0nmpubA4/HW7V9IuamZcOGDZyFp729Heeeey7uuOMO3H333UR4AoiAFB+LxQKDwcD+m+sSEzN8mZmZiYKCAvaNZzAY2LtulUrFOj2npKQEzCYyYx00NDQUlPtTVquVzVTxpDGCudgxnXMhISHsTcJqes7p9Xq0tLRAKBQG5TKnXC6HVCr12u7HltXcJxoeHsbo6KhXwtPV1YVzzjkHN910Ex544AEiPAFGQIrPlVdeicHBQezatQsXXHABMjIyPH7jjI+Po7e31+XwJTOvwtx1x8TEsEK0Vss/tj5ngdBK7SlmsxlSqRQURaG6uprzRclZ5xxz1+1Pzzlmfy0YBzCBxWXrtrY2FBcXIz093S/HYPaJmIrVl/tEjPDU1dVx3pvt7e3FOeecg6uvvhqPPPJI0P0NTwYCUnzGx8fxzjvv4L333sPBgwexYcMG7Ny5Ezt37sS6detWfCMxswCTk5OorKz0yBnZbDazHya5XM4u/6SkpLD5OP7GarWivb0dOp0uIFupXeGvpSrHzjmj0QixWMxe7HzVOcfMIKWnp9tVy8ECE6vub585R5h9IsZ3LjIyktM+EeNq7o3wDA4OYvv27bjkkkvw+OOPB13VerIQkOLDQNM0pqam8P777+O9997D119/jcrKSlaIHC8OzIVbq9Wiurraq7svx8HJsLAwpKSkIDk52W/7EEwYXrC0UjvCVAzempu6wrY7a2Zmxmedc8zmfE5ODnJzc3181v5nenoaHR0da56DtNw+kSuXdGaZua6ujnO1PzIygnPOOQfnn38+nn76aSI8AUxAi48tNE1jbm6OFaJ9+/ahuLiYFaKIiAjceOON+M1vfoMtW7b49MJttVrZfYjZ2Vl2HyIlJQXx8fE+ESKmMYIJwwu2Dw0Topaeno7CwsJVrRj0ej1bsapUKsTGxrL7RO7egDB7JN5szq8lTGNKZWVlQO0PurtPNDY2hsHBQa+EZ3x8HNu2bcPZZ5+Nv/71r0H3GTrZCBrxsYWmaSiVSvz73//Gu+++i88++wwURSE/Px9/+9vfUFdX57c3nu0+xMzMDHg8HpKSkpCSkoKEhAROx1WpVJBIJMjIyAjKpR7mwp2fn+9RiJo/cNY5x7RwL1exMjlGwRilAQCTk5Po6elZE48/T1hunyg0NBQKhQJ1dXWIi+OWIzQ1NYXt27fj1FNPxQsvvBB0nYknI0EpPrZ88MEH+PnPf44dO3bAaDTi888/R1paGnbu3Ildu3ahpqbGr0KkUqnYoVbGSsYTvznG6ifY77gD8cK9XOdcUlISe6PAXLjLy8uRnJy81qfsMRMTE+jt7UVVVRUSExPX+nQ8wmAwoL+/n03htG2x92SfaHp6Gueccw42bNiAV155ZVWF57nnnsPjjz8OmUyGqqoqPPPMM9i0aZPT5+7evRtXX3213WPh4eF2nb0nE0EtPlKpFKeccgpeffVV1hJdo9Hgk08+wbvvvotPP/0UIpEIF1xwAXbt2oWNGzf67Y3JbIhPT09jZmYGZrOZFSKxWOz0uKOjoxgcHAzKVmpgcalkYGAg4O+4gR8qVuaum6IoREVFQaPRBNxSlbscP34c/f39qKmpWdNIB64wWUjMDBiXfaK5uTmce+65KC0txeuvv76qQ8BvvvkmrrjiCjz//POor6/HU089hbfffhu9vb1Ob2R2796NX/3qV+jt7WUf4/F4a7o/t5YEtfgAix/A5SoGnU6Hzz77DO+++y4+/vhjREdH4/zzz8euXbvQ2NjotzcqTdNYWFhghchgMLAtwklJSQgJCUFfXx9rlsp1qWGtYLy2JiYmUFNTE3Tnz5jVTk5OIiwsDGazmc2/8WXnnD9h9khsXSOCCUZ4nAmnu/tECoUCO3bsQF5eHt58881Vdy2pr6/Hxo0b8eyzz7LnnZWVhVtuuQV33333kufv3r0bt956K1Qq1aqeZ6AS9OLjLgaDAV9++SXee+89/Otf/4JAIMD555+PCy+8EKeccorfLjjMOjcjRFqtlj1WMM7wUBSF7u5uKBQK1NbWBpQVjjswrfhTU1PsHbezzjmmag1E9wsmx6m2tjbohB/4YanQnYrNdp9odnYWk5OTePTRR3Hqqadi3759yM3NxXvvvbfqRq8mkwlRUVF45513sGvXLvbxK6+8EiqVCv/617+WfM/u3btx3XXXISMjAxRFoba2Fo888gjKyspW8cwDh5NGfGwxm83Yv38/3n33XXzwwQewWq3YsWMHdu3ahS1btvjtjWwymdDc3AyLxYLQ0FC7FuHk5OSAd0pm4hwMBgNqamoC8sK8Eozdj1wuX1Y4fdE5508Yy5lAC7FzF2aPrbq62qMZPIa5uTn87//+L55++mnodDoUFBSwHa8NDQ2rtt8zOTmJjIwMHDx4EI2Njezjd955J7766iscPnx4yfccOnQI/f39qKyshFqtxhNPPIGvv/4anZ2dQWed5QtOSvGxxWKx4Ntvv8Xbb7+NDz74AFqtFjt27MDOnTtx5pln+mzIk0nuZOxaQkJClphrxsXFISUlBUlJSQE3XMrEWwBAdXV1UCxN2UJRFDo6OrCwsIC6ujq3hNOxcy4iIoIVotX2nLN1d66trQ06V3ZgsSOtu7ubs/AAi3u6F110EcLCwvDGG2/g22+/xb/+9S98+umn6OzsXLW9Oy7i44jZbEZJSQkuvfRSPPTQQ/483YDkpBcfW6xWKw4dOoR33nkH77//PpRKJbZv346dO3fi7LPP5nzny7RSrzQDYzQaWSFSKpXsHXdKSgrn4CxfYTAY2HiLioqKoGtjZSo221woT3Gnc85f2ObZeOPuvJYwwuNNV55Op8NPfvITUBSFTz75xO73wLjerxZclt2ccfHFF0MgEOCf//ynn840cCHiswwUReHo0aOsEE1NTeHss8/Gzp07cc4557h95zkzM4OOjg6PWqlt77jlcjmio6Pt/OZW845bo9GgtbUViYmJKC4uDrrBPYvFAolEApqmfVaxURQFpVLJ3ixQFOVRkq4n0DSNvr4+TE9Po66uLiCW/jxFJpOhq6vLK+ExGAz42c9+Bo1Gg88++ywglhzr6+uxadMmPPPMMwAW3xfZ2dm4+eabnTYcOGK1WlFWVoZzzz0XTz75pL9PN+Ag4uMGFEVBIpGwQjQyMoIzzzwTO3fuxI4dO5adSWBakb2ZITGbzXY2PxEREazNT2xsrF+FiKnYMjMzgy5HCPjBrig0NBRVVVV+qdiYFnvmZsFgMPisc46mafT09GBubg51dXVrXgFzgbH8qaqq4tyObzQacfnll2N2dhaff/55wLSVv/nmm7jyyivxv//7v9i0aROeeuopvPXWW+jp6UFKSgquuOIKZGRk4I9//CMA4MEHH0RDQwMKCgqgUqnw+OOP44MPPkBzczNKS0vX+KdZfYj4eAhN0+js7GSNT3t6enD66adj165d2LFjBxITE0FRFF5++WUUFBT4tBXZarVibm4O09PTrN8cswfh65Cv2dlZtLe3o6CgwO0QskCCWSqMjo5GRUXFqlRsy3nOcemco2kaXV1dUCqVqKurC7g9QHdghMebOSqz2YwrrrgCo6Oj2Lt3b8AN0j777LPskGl1dTWefvpp1NfXAwC2bNmCnJwc7N69GwBw22234b333oNMJkNCQgLq6urw8MMPo6amZg1/grWDiI8XMEsi7777Lt599120tbWhqakJMpkMCwsL+O677/w2QGa1WqFQKDA9PW3nN5ecnIyEhASvhGhychLd3d2r7ozsK5jmjoSEBJSUlKzZUuFynXNJSUkr7tswNzhqtdrt5ohAg7Es8kZ4LBYLrrnmGvT09GD//v1BOQhMWB4iPj6CpmkcO3YMF198Mebm5qDX67F582ZccMEF2LlzJ9LT0/22bMXsQTBCRNM0K0Qikciji+/IyAiGhoaC0q4FWNyjam5uRmpqKtavXx8wS4Umk4ldPpXL5ct2zjFdeRqNBnV1dQHffu8MJtahoqKC83Kz1WrFf/7nf6K1tRX79+8PypsgwsoQ8fERw8PD2LZtGyorK/Hqq69ibm4O7777Lt577z0cOnQIGzduZG1+srOz/XZRZExXmaUfq9Xq1ma47fBlMA6/Aj84a2dlZSEvLy9ghMcRZvmUGZwMCQlhp/fHx8eh1+tRV1e36hP7voARHm9iHaxWK2655RZ89913OHDggM+SWAmBBREfHzE5OYkXX3wR//3f/21XadA0jcnJSTYK4ptvvkFlZSV27dqFnTt3+nUjn6ZpzM/Ps+4KJpOJtfkRi8WsvRBFUejq6oJKpUJtbW1Qbmwzkel5eXlr7qztCbZV69TUFCiKQnJyMlJTU5f1BAxU5ubmIJVKvRIeiqJw6623Yt++fdi/f39Q/S0JnkHEZxWhaRozMzP44IMP8N5772H//v0oLi5mhcifkc00TUOj0bBCpNfrkZiYCLFYDJlMBovFgpqamqBd5mlvb0dRUVFQ3iVbrVZIpVKYTCYUFhaykR22nXNisTigKyEmuru0tJTzEhlFUbjzzjvx0Ucf4cCBA8jLy/PxWRICCSI+awSzPPavf/0L7777Lr788kvk5eWxURBlZWV+3SjXaDSYmprC2NgYKIqCSCRiW7gD+SLnCBPpsNbpnVyxWq2QSCSgKAo1NTVsNeos+yY+Pp5tWAik7jcmz8lb4bn33nvx9ttv48CBAygsLPTxWRICDSI+AYJarcaHH37IhuNlZGSwQlRdXe1zIdLr9WhpaUFMTAzy8/PZzfD5+XnEx8ezNj+B3GnFOCMHQ6SDMywWC1pbW8Hj8VBdXb2iy7rBYGD38VQqFWJiYuw859Zqf0uhUEAikaCkpIRznhNN03jwwQfxyiuv4MCBAyguLvbxWRICESI+AcjCwoJdJpFYLGYduDdu3Oi1EC0sLKC1tRVJSUlLlvqYi9z09DTUajWEQiFbEQXS3Tbj7FxdXR0wQ4eeYDab0draipCQEFRXV3u0t7Nc55ynIWzewghPcXEx0tPTOb0GTdP405/+hOeffx779+9HeXm5j8+SEKgQ8QlwdDod9uzZw2YSxcTEsF1zjY2NHm9IK5VKSCQSrFu3Drm5uSteqIxGI2ZnZzE9PQ2lUomYmBhWiNbK5oUx2BwfHw9aZ2ez2YyWlhafOC8s1znHzHv5a+lWqVSitbXVa+H5y1/+gr/85S/Yu3cvqqurfXuShICGiE8QYTAY8MUXX7CZRGFhYWxFtHnzZpdWLozP3Pr16z22cDebzawQ2frNJScnIyYmZlXutmmaRm9vL2ZmZtgsnmDDZDKhpaUFERERqKys9Kk42HrOzc7Owmq12nU3+qpzjhEebxo8aJrGs88+i0cffRSfffYZNm7c6JNzIwQPRHyCFJPJZJdJRFEUzjvvPDaTyLFpgNkf8cZnjsFisdjZ/KxG1IBtO3iw2s0weU6MO7i/nbDn5+fZfSKmc84xDdRTVCoVWlpaON3A2J7b3/72N/z+97/Hp59+ahdJQDh5IOJzAmCxWPDNN9+wmUR6vZ7NJDr99NPx4IMPwmKx4L//+799vj9itVohl8tZIRIIBKwQxcfH+0SIKIpCW1sb9Ho9amtrg7Id3Gg0orm5GbGxsX7vZHSGRqPxunNOpVKhtbUVBQUFbju0O0LTNHbv3o177rkHH330EU477TROr0MIfoj4nGBYrVYcPHiQdeCWyWTg8Xj47W9/i5tuusmvA6QURbGZN7Ozs+DxeHZ+c1wuuEwrssViQW1tbdCF2AGLy6XNzc2Ii4tDWVnZmjsvME0ls7Oz7F6eq845tVqNlpYWr4XnH//4B+644w78+9//xumnn+7tj0IIYtZcfJ577jnWFbaqqgrPPPMMNm3atOzz3377bdx3330YGRlBYWEhHn30UZx77rmreMbBgdFoxM9//nMcPnwYZ511Fvbv34/p6WmcddZZ2LVrF7Zv3+7XNEzHzBuapu1sftwRIqYjjM/nu2xFDlT0ej2am5shEolQUlKy5sLjCLOXZ9s5x/ydmM45Rnjy8/M5O5zTNI233noLt9xyC959911s27bNxz8JIdhY02SwN998E7fffjseeOABtLS0oKqqCtu2bcPMzIzT5x88eBCXXnoprr32WrS2tmLXrl3YtWsXOjo6VvnMA58bb7wRo6OjOHbsGP7+97+jv78fX331FYqLi/HII48gJycHP/vZz/D6669DpVLB1/cgfD4fiYmJKCkpwWmnnYaqqioIBAL09PTgq6++Qnt7O+s95wyj0Yhjx44hNDTUbvgymNDpdDh27BjEYnFACg8AhIaGIj09HdXV1diyZQsKCwvZHKSvv/4aUqkUx44dQ25urlfRGu+//z5uvvlmvPHGG6sqPM899xxycnIQERGB+vp6HDlyZMXnv/322yguLkZERAQqKirwySefrNKZnnysaeVTX1+PjRs34tlnnwWweLeclZWFW265xWkS4M9+9jNotVp89NFH7GMNDQ2orq7G888/v2rnHQwMDw8va91P0zQ6OjrYTKK+vj67TCKRSOR3vzlmlshoNEIsFiMlJYX1m2MGYIVC4Zrsj/gCrVaL5uZmpKSkBJS7trtQFIWJiQn09vayXXJM51xiYqJHNwMfffQRrr76avzjH//AhRde6K9TXsKbb76JK664As8//zzq6+vx1FNP4e2330Zvb6/TppuDBw/itNNOwx//+Eecd955eP311/Hoo4+ipaWFzB/5gTUTHy4Z6NnZ2bj99ttx6623so898MAD+OCDDyCVSlfhrE88mPZlJpOovb0dp512Gnbu3Inzzz8fycnJfvebY4RIr9cjLi4OGo0GSUlJKC0tDbqLNvBDrEN6ejoKCgqC8mdYWFhAc3MzcnJysG7dOvaGYXZ2Fvr/v70zj2rqWtv4E2YQAUGQUQZBrQOCICgq2pYromLQWlsnHNA6FJemfpXaIt6qONDaq6UqdajWJU5VqF6xKLOCSMvgBKKCIIgSBGQIUyDZ3x/enJqCyBCSAPu3VtYq5+x98u60Pc/Z+7z7eevqoKuryyQstJY5FxkZiUWLFuHYsWOYO3euFEdAH27lHZk9UpaWlkIgEDTz4xowYACKi4tb7FNcXNyu9pR3w2KxMHToUHzzzTdIS0vDgwcPMGXKFISGhsLGxgYeHh44ePAgioqKJL40x2Kx0LdvXwwaNAguLi4YOXIkKisrwWKx8OLFC2RkZODZs2fg8/kS/d6upLq6GqmpqTA1Ne32wmNubg4LCwuwWCxoa2vDxsYGLi4uGDt2LHR0dPDs2TNcv34dqampKCgoQF1dndh1YmJi4O3tjUOHDuHjjz+W6hhEae1ubm7MMQUFBbi5uSE5ObnFPsnJyWLtAcDd3f2t7dtDeXk5MjMzO32dnkT3W0indBksFgvW1tbw8/PDxo0bUVBQwNQk8vPzw5gxY8Bms8FmsyVek6iiogKZmZmwsrKCpaUl6urqwOVy8fz5c2RnZzOpwe0tRy1NqqqqkJ6ezrhHdEdEs7aBAwe+dQx9+vSBpaUlLC0tUV9fzyQsPHr0CLGxsWhqaoK1tTX8/f0RHByM+fPnS12EW3u4zc7ObrFPVz3cvnz5EqNHj0ZRURHi4uIwadKkTl2vpyCzmY9oxzWXyxU7zuVy3+qMa2ho2K72lI7DYrFgbm6OL774Ajdu3MDTp08xf/58XL16Fba2tpg0aRJ++OEH5ObmdnpGVFZWxqTxim546urqsLCwgJOTEyZMmAADAwOUlJQgMTERf/75J/Lz81FbWyuJoUqEyspKZpmquwuPqBhfW1BTU4OZmRkcHBwwadIkDBs2DElJSeBwOOjTpw+ysrKQnJwMoVDYxdHLJ0KhEBMnToSVlRWWLVuG2bNnIyoqStZhyQUyEx8VFRU4ODggJiaGOSYUChETE/PWHc/jxo0Taw8AUVFRdId0F8NisWBiYoK1a9ciNjYWhYWFWL58Oa5fvw4HBwe4uLhg9+7dyM7ObrcQlZSUMK7Ib9s/oqamhoEDB8LR0RGurq4wNjZGeXk5bt68iVu3buHJkyfg8XiSGGqHEO36HzRoECwsLGQWR2cQJUiYmJhg0KBBHbqGsrIyBg8ejLy8POzZswchISEoKSnBjBkzsGzZMglH3Dry8nCroKCA2NhYJCQkYNOmTWCz2Zg7dy7NooOMs93Onj2LxYsX4+eff4aTkxP27t2Lc+fOITs7GwMGDIC3tzdMTEywc+dOAK+zUSZNmoRdu3Zh+vTpOHPmDHbs2EGzUWQEIQTl5eViNYmsra2ZUhDDhg1rNVNNtKTWUcuff+5RUVdXh4GBAQYMGCA1vzmRs3Nn7GZkTU1NDVJTUxnh6ejvlp6eDk9PT2zevBkcDoe5TmNjI169etVpW6f24uzsDCcnJwQHBwN4/XA7cOBA+Pr6vjXhoLa2Fv/973+ZYy4uLrC1te1wwoFQKASLxWJ+i5ycHHz33Xc4e/Ysfv31V7DZ7A5dtycg802mP/30E7PJ1M7ODj/++COcnZ0BAJMnT4aFhQWOHz/OtP/tt9/g7+/PbDINCgqim0zlAEKIWE2ia9euwdTUlBGiUaNGiQlRbm4unj59Cjs7O+jq6nb6+0V+cyUlJSgtLYWKigojRF3lNycqotZdK6gCf894jIyMOpUgcffuXUyfPh1ffvkl/Pz85CLRQp4ebgkhzG/y5MkT7NmzBydPnsSRI0eknowhL8hcfCg9k+rqakRERODChQuIjIxE//79MXPmTLDZbISFhSE1NRXh4eHQ1taW+HeL/OZEqcGKiopiNj+SuDGKykZ3poiarBFtgjU0NISNjU2Hf5esrCx4eHjA19cXAQEBciE8ImT1cCsQCJq5iAuFQuYBLD8/Hz/88AOOHz+OkJAQzJ8/v+OD7KZQ8aF0OTU1NUxNovPnz0MgEMDLywurVq3C2LFjJWb13xJCoRDl5eWMzQ+LxYK+vj4GDBjQYb85UWmKzpSNljW1tbVIS0uDgYFBpzbBPnz4EB4eHvDx8cH27dvlSnhkxZsic+XKFbx69QpTpkxpZitVUFCAffv24fDhwwgODsbixYtlFbJM6H5bx7uQ9lhxHD58GBMnTkS/fv3Qr18/uLm5vdO6o7fSp08feHl5QVNTE0ZGRjhw4AD69u2LTz75BIMHD8b69esRHx+PxsZGiX+3goIC+vfvj2HDhsHV1ZUpZXD//n0kJCTg/v37TO2btsDlcnHv3j2MGDGi2wqPyG+us8KTk5ODGTNmYOHChdi2bRsVnv8hEhgfHx8sWbIE69evh52dHY4fP45Xr14x7QYOHAgOh4OVK1eCw+Hg0KFDsgpZJtCZz/9orxXHggULMH78eLi4uEBNTQ27d+9GeHg4MjMzu+36f1dy5MgR7NmzB1FRUcyLeT6fj9jYWKYmEQCmJtGkSZM6XHOmLYjeUXG5XJSUlKCxsVHM5qel2diLFy/w4MEDjBw5Evr6+l0WW1dSV1eH1NRU6OvrY8iQIR0WjPz8fEydOhVeXl7Yu3dvt7RAkjSi9zqEEGRkZGDt2rUICQmBpaUlvvzyS1y9ehXr1q3DwoULoaenx/QTCoXw9fVFSEgI0tPTe01FVyo+/6O9Vhz/RCAQoF+/fvjpp5/g7e3d1eF2OwQCAaqqqt5aT6ipqQnXr19nahLV19djxowZYLPZ+OCDD7p0YykhBNXV1YzNT319vVgFUGVlZSYzb9SoUWI3ju5EfX09UlNToaenh6FDh3ZYeAoLC+Hu7o6pU6fiwIEDVHggvtRWV1eHwsJCHD58GN999x3ThsPhIDw8HOvWrcOiRYvQv39/AK/3V/Xv3x8+Pj7Yt29ftzTR7QhUfNAxn7l/Ul1dDQMDA/z222+YMWNGF0bb8xEIBEhKSsL58+fx+++/o7KyknnK/te//tWlNYkIIaipqWFmRDU1NdDQ0EBtbS1sbW2lni4sKUTC09nSDi9evIC7uztcXV1x+PDhLn1f1x3ZsmULoqKikJ2djeHDh+PSpUtiD1xfffUVs8qyYcMGaGlpoaGhAbt27YK/v3+v+j2p+OD1fhMTExPcvHlTbMPqxo0bkZCQgJSUlHdeY82aNbh69SoyMzPl1v6lOyIUCpGSksIUxyspKcGUKVPg5eUFd3f3Lq1JBLxOCc/Pz4eamhrq6urQr18/JnOuu1RUFRWz69evX6eEh8vlwsPDA2PGjMHx48d71Y3ybbyZQh0aGgpfX198++23SEhIwK1bt7Bw4UKsX79eLCNy7dq1aGpqwsGDB8VmTL0NKj7ovPjs2rULQUFBiI+Ph62tbVeH22sRCoVIT09nSkEUFhbCzc0NXl5emDZtmsT38zx9+hRPnjyBvb09dHR0UFdXx2TNVVZWQltbmxGitpailjaiukg6Ojqdcgl/+fIlpk+fjuHDhyM0NLTXLA21lbi4OFy5cgX29vZM2vSWLVtw+fJluLm5Yd26dTA2Nm7W703x6m30Tsn9Bx2x4hDx/fffY9euXbh27RoVni5GQUEBjo6O2LVrF7Kzs5GSkgJ7e3v85z//gYWFBebMmYMTJ06grKys035zeXl5ePLkCUaPHg0dHR0Ar/3mzM3NMWbMGEycOBGGhoYoLS1FUlISUlJSkJeXh5qaGgmMVDI0NDQw5bs7Izzl5eXw9PSEjY0NTp482euFZ926dWIPpGlpadiwYQOOHTsm9ht/++23YLPZiI6Oxr59+5Cfny92nd4sPAAVHwAd85kDgKCgIGzbtg2RkZFwdHSURqiU/6GgoABbW1ts3boV9+7dw+3bt+Hi4oKff/4ZVlZWYLPZOHr0KFPCuz2I3BccHR3fuglWVVWVMdR0dXWFqakpKioqkJycjOTkZOTm5oLH40m8DEVbEZUUEBXk6+hNrqKignExP3v2LJSVlSUcafdi4cKF+P3338X870aPHo2FCxdCR0cHR44cwYsXL5hzAQEB+PjjjxEaGorIyEixa/Vm4QHoshtDe604du/ejYCAAJw6dQrjx49nrqOpqdli9VCKdCCEIDc3l1may8jIgIuLC9hsNmbOnAkjI6O3/k8v6ltUVAQHB4cO/XtsbGwUs/lRU1NjbH769u0rlRsOn89Hamoq+vbtixEjRnT4O6uqquDl5QVtbW1cvHix17/LLCoqgo2NDVxdXXH58mUoKSmJvbPZv38/Tp48iaFDh2L79u1iWy7OnDmDTz/9VFahyyVUfN6gPVYcFhYWePr0abNrbNmyBf/+97+lGDXlbRBC8PTpU1y4cAHh4eG4desWnJycmJpEZmZmzI1ZKBTi4cOHKCkpgaOjI/r06dPp7xcIBCgtLQWXy0VpaSmUlZUZIdLW1u4SIRLNePr06YMRI0Z0+GU2j8fD7NmzoaKigoiICLl9pyVt/vrrL3h6esLZ2RnHjh2Drq6u2PLZ/v37cfr0aVhaWiIwMBADBw4U69+S7U5vhYoPpVdACEFRURHCwsIQFhaGpKQk2NnZwcvLC56enti5cycaGhpw6NChLknlFggEYjY/b/rN6ejoSCTjSSQ8GhoajJNDR6itrcWcOXNACEFERASdyf+DjIwMeHh4wMHBASdOnICenp6YAIWEhODs2bNQU1PD0aNHW0w0oFDxofRCCCHgcrkIDw/HhQsXEBsbC0VFRaxYsQIrVqzolOVMWxAKhXj16hW4XC5evnwJQggjRLq6uh0SjcbGRqSlpUFdXb1TwlNfX49PPvmE8ePT0tLq0HV6Ovfu3cPUqVMxfPhwnDx5EgYGBmICtG/fPty9exchISG9/j3Z26DiI8fs37+fWQYcNWoUgoOD4eTk9M5+Z86cwbx588BmsxnbGkpzBAIBli9fjvj4eKxevRrx8fGIiYmBjY0NZs6ciVmzZuG9997r0n0YhBBUVFQwm1oFAgH09fVhYGAAPT29Ni3RiIRHTU0Ntra2HY63oaEBCxYsQGlpKa5du8Zk+VFaJjs7G+7u7rCyssLp06dhaGgoJkBNTU3N3gtR/oaKj5zSXq85Efn5+ZgwYQKsrKygq6tLxacVgoKC8MsvvyAmJgYmJiaM39ulS5eYmkQDBw5khKgzN/a2QAhBVVUVI0R8Pl/M5qelFOfGxkakp6dDRUWlWc2k9sDn8+Ht7Y3CwkLExMRIpMZSbyAnJwfu7u4wNjbGmTNnmvk60nc8b4eKj5zSEa85gUAAV1dXLFu2DDdu3EBFRQUVn1bg8XioqanBgAEDWjxfVVUlVpPIwMCAESIHB4cuFyIej8cIUV1dHfT09GBgYAB9fX0oKyujqakJ6enpUFZW7pTwNDY2wsfHBw8fPkRsbGy3NU2VNKIZS2NjY6tLZ3l5eZg6dSp0dHQQERGB/v37Iy4uDu+//74Uo+1+0LmgHCJ6cezm5sYcU1BQgJubG5KTk9/ab+vWrTAwMICPj480wuz2aGpqvlV4AEBLSwvz5s3D+fPnweVyERQUhJKSEsycORPDhg3Dxo0bcfPmzTaXY2gPLBYLffv2hbW1NVxcXODs7AwtLS0UFBQgISEBaWlpuHXrFrPfqaPC09TUhFWrViErKwvR0dEyF57y8nIsWLAAWlpa0NHRgY+PD3g8Xqt9Jk+ezJSqFn1WrVrV6VgUFBQQHx+Pbdu2tdrO0tIS0dHR4PF4YLPZ8PT0REBAgFxtOJZHqPjIIaWlpRAIBM1ujAMGDEBxcXGLfRITE3H06FEcPnxYGiH2Ovr06YM5c+bg1KlTKC4uRnBwMKqrqzF37lwMGTIEHA4HCQkJaGpq6pLv19TUhJWVFcaOHQtnZ2fU1taisbERFRUVyMjIQEFBAerr69t1TYFAgLVr1yItLQ3R0dGtCrG0WLBgATIzMxEVFYXLly/j+vXr+Oyzz97Zb8WKFXjx4gXzCQoKkkg8t27dYjaHtvaQYWZmhujoaLx69Qr37t3DiRMnJJKu35Pp3T4ZPYTq6mosWrQIhw8fZmzaKV2Huro6s1eIz+cjOjoaYWFh8Pb2BovFwvTp0zFr1iy4urpKvCZRU1MTsrOzoaGhATs7OzQ2NjKlIB49egQtLS1mL1Fre3OEQiE4HA4SExMRFxcnF+nADx48QGRkJP766y/GMSQ4OBjTpk3D999/32qMGhoaEinu90/LG2NjYzx//hxCofCd726MjIxw48YNNDQ0yMXvKe/QmY8c0l6vOZHzsqenJ5SUlKCkpIQTJ07g0qVLUFJSQm5urrRC73WoqKhg2rRpOHLkCJ4/f47Tp09DVVUVK1euhJWVFVauXIk//vij3bOSlhAIBLh9+zYUFBRgZ2cHRUVFqKmpYeDAgYzfnLGxMcrKypCUlIRbt2616DcnFAqxceNGREVFITo6utlGSFmRnJwMHR0dMasqNzc3KCgovNPcNzQ0FP3798eIESOwadMm1NbWdigGFouF4uJiZGZmAgDs7e1hbGyMvLw8po1QKGT++Z+vzPX09KjwtBE685FD3vSaE9UXEnnN+fr6Nms/dOhQ3Lt3T+yYv78/qqursW/fPpiZmUkj7F6PsrIyPvzwQ3z44YfYv38/EhMTcf78eaxfvx5VVVXw8PCAl5cX3Nzc2r2RVSAQICMjAwAY4fknqqqqMDU1hampKRobG/Hy5UtwuVzk5uaCxWLhjz/+wEcffYSLFy/i0qVLiIuLg6WlpUTGLgmKi4ubZXIqKSlBV1f3rcvNADB//nyYm5vD2NgYd+/ehZ+fHx4+fIiwsLB2x1BWVgYnJyfU19fD0NAQDQ0NyM3NxdGjRzF+/Hg4ODhATU0N6urqUFVV7fX+bJ2CUOSSM2fOEFVVVXL8+HGSlZVFPvvsM6Kjo0OKi4sJIYQsWrSIfPXVV2/tv3jxYsJms6UULaU1BAIBSUpKIhwOh1haWhJNTU0ye/ZscuLECcLlcklNTU2rn6qqKnL9+nUSHx9Pqqqq3tn+n5/KykqSmJhI3n//faKoqEgUFRXJ8uXLyZ9//kmEQmGXj9/Pz48AaPXz4MEDEhgYSAYPHtysv76+Pjlw4ECbvy8mJoYAIDk5OR2KNyMjgzx+/JgcPXqU7Nu3j7BYLKKmpkbGjh1LdHV1iZ6eHmGz2aSqqqpD16e8hs585JRPPvkEL1++REBAAOM1FxkZybwULigooBvXugkKCgpwcXGBi4sLvv/+e6SlpeHChQvYtm0bVq5cCTc3N7DZ7BZrEgkEAty5cwdCoRD29vYd2jOipKQEOzs7uLi44N69e/jmm2+QmpoKNzc36Ojo4MqVKxg+fLgkhyzGhg0bsGTJklbbWFlZwdDQECUlJWLHm5qaUF5e3q73OSI/xpycHDH36bZiZ2cHALC2tgbwOpW6pKQEhw4dwt27d8Hj8WBgYNDlhQx7PLJWPwqltyIQCEhGRgbx9/cnw4YNIyoqKsTDw4McPHiQFBYWEi6XS9hsNjl37hyprKxs94xH9OHxeGTr1q1EV1eX3L59m/n++vp6EhERQWpra2X4K/xNVlYWAUBSU1OZY1evXiUsFosUFRW1+TqJiYkEALlz506n4mlqaiKEELJx40YyduzYZucFAkGnrt/boZtMKRQ5gBCCBw8eMKUgMjMzoampCXV1dfzxxx+wtrbu0PsFQgiCg4MRFBSEa9euyX3dKQ8PD3C5XISEhKCxsRFLly6Fo6MjTp06BeB1WYMPP/wQJ06cgJOTE3Jzc3Hq1ClMmzYNenp6uHv3LjgcDkxNTZGQkCCRmBISErBy5Ur89ddfdLYjSWSrfZTuxE8//UTMzc2JqqoqcXJyIikpKa22f/XqFVmzZg0xNDQkKioqxMbGhkREREgp2u5LfX09+eCDD4iJiQmxs7MjSkpKxNXVlfzwww8kJyeH8Hi8Ns949uzZQ7S1tUlycrKsh9UmysrKyLx584impibR0tIiS5cuJdXV1cz5vLw8AoDExcURQggpKCggrq6uRFdXl6iqqhJra2vy5ZdfksrKSonFlJSURJSUlEhBQYHErkmhMx9KG2mv1xyfz8f48eNhYGCAr7/+GiYmJnj69Cl0dHQwatQoGYygeyAQCPDRRx/h2bNniI6Ohra2NvLz85maRCkpKXB2dmb2GZmamrY4IyKE4NixY/j6668RERGBiRMnymA0PQM+n4+8vDwMGTJE1qH0LGQsfpRugpOTE/n888+ZvwUCATE2NiY7d+5ssf3BgweJlZUV4fP50gqxx3DkyBFSVlbW7LhQKCQFBQVk7969xNXVlSgqKpIxY8aQwMBAcv/+fWZGxOPxyMGDB4mmpiYzQ6BQ5A0686G8Ez6fDw0NDZw/f57ZdwQAixcvRkVFBS5evNisz7Rp06CrqwsNDQ1cvHgR+vr6mD9/Pvz8/KjLrwQghKC4uBjh4eEICwtDQkICRowYATabDVVVVQQGBiIsLAxTpkyRdagUSovQVGvKO2nNay47O7vFPk+ePEFsbCwWLFiAK1euICcnB2vWrEFjYyO2bNkijbB7NCwWC0ZGRlizZg1Wr16NsrIyXLx4EadOnUJsbCxOnjxJhYci11DxoXQJQqEQBgYGOHToEBQVFeHg4ICioiJ89913VHwkDIvFQv/+/eHj44Nly5ahqKgIpqamsg6LQmkVKj6Ud9JerzngtcmisrKy2BLbe++9h+LiYvD5fIkbblJew2KxqPBQugV0izzlnbzpNSdC5DU3bty4FvuMHz8eOTk5YiaMjx49gpGRERUeCoVCxac78eaNXNp88cUXOHz4MH799Vc8ePAAq1evRk1NDZYuXQoA8Pb2xqZNm5j2q1evRnl5OdatW4dHjx4hIiICO3bswOeffy6rIVAoFDmCLrt1I2Tp5dZerzkzMzNcvXoVHA4Htra2MDExwbp16+Dn5yerIVAoFDmCplp3AwoLC7Fy5UqsXbsWHh4esg6HQqFQOg1ddpNzysvLce7cObx8+ZIpy9taOV8KhULpDlDxkXMuX76MzZs3IysrC2FhYSgsLGy2SVMkRnFxcZg9ezaOHTsGPp8vi3Clzv79+2FhYQE1NTU4Ozvjzz//bLX93r17MWTIEKirq8PMzAwcDkciVUYpFEo7kam/AuWdlJSUEHt7ezJz5kzGUuXx48dibUTW70uWLCG6urpETU2t1UJzPYUzZ84QFRUV8ssvv5DMzEyyYsUKoqOjQ7hcbovtQ0NDiaqqKgkNDSV5eXnk6tWrxMjIiHA4HClHTqFQqPjIOUePHiVjxowh165dI4SQVqsn2tjYkKCgIELI34LUk2mv39znn39OPvjgA7FjX3zxBRk/fnyXxkmhUJpDl93knLi4OJiYmGDw4MEAAE1NTbHzovTrqKgo8Pl8xnm3paU5WaZqSxo+n4+0tDS4ubkxxxQUFODm5obk5OQW+7i4uCAtLY1Zmnvy5AmuXLmCadOmSSVmCoXyN1R85JgXL17g8ePHGD58OMzNzQGgmX0++V+y4m+//QZra2sMGzYMwN+iJHr3o6io2CxVu7CwEKNGjUJQUBDKysq6dCySpjW/ueLi4hb7zJ8/H1u3bsWECROgrKyMQYMGYfLkyfj666+lETKFQnkDKj5yTFJSEgQCAVN9sqWZi2iGc/36dYwbN46xVlFQUEBiYiI2bNiAUaNGYenSpWIzAkIITE1NwWazERAQgHnz5klhRLIlPj4eO3bswIEDB5Ceno6wsDBERERg27Ztsg6tWxAYGAgXFxdoaGhAR0enTX0IIQgICICRkRHU1dXh5uaGx48fd22glG4BFR85RkVFBTweDyYmJgCabzIViVF8fDxqa2vh6OgINTU1AEBDQwNWrFiBvLw8rFu3Dnw+H/PmzcPRo0fR1NQE4PUsas6cOXBychJbvuoOdMRvbvPmzVi0aBGWL1+OkSNHYtasWdixYwd27tzZo5Ykuwo+n4+PP/4Yq1evbnOfoKAg/PjjjwgJCUFKSgr69OkDd3d3mmFIoeIjz4wbNw79+vXDvHnz8H//939oaGgQO//mktugQYPw3nvvMecKCgqgqamJuXPnYtmyZQgNDcXp06dhZWUFJSUlZvnuxo0bKCkpwfTp06U3MAnQEb+52traZgIumjkSutf6nXz77bfgcDgYOXJkm9oTQrB37174+/uDzWbD1tYWJ06cwPPnz/H77793bbAUuYeKjxyjr6+PmzdvYsuWLaipqWmWRCD6Oy4uDuPGjYOZmRlzztTUFKNHj8aGDRuwZ88elJeXY9y4cXBxcWHalJeXIyMjAyYmJhg+fLh0BiVB2us35+npiYMHD+LMmTPIy8tDVFQUNm/eDE9PT1rgrgvIy8tDcXGx2KxaW1sbzs7Ob00KofQeqLebHCMUCqGgoIBFixZh0aJFLZ67efMmqqur4ejoCHV1dea8uro6fv75Z4wdOxbnz5/Hs2fPEBgYCA0NDabvo0ePkJWV1e1mPSLa6zfn7+8PFosFf39/FBUVQV9fH56enggMDJTVEHo0osSP9iSFUHoPVHzkGNGNUyAQNHsy/2eWmygVGwDu37+PZ8+eYerUqVi6dCn09PSwfPlyjBgxAj4+Psx179y5g/Lycnh6ekppRJLH19cXvr6+LZ6Lj48X+1tJSQlbtmyhxeze4KuvvsLu3btbbfPgwQMMHTpUShFRegtUfLoBLS0JiY5dunQJnp6eGDFiBHPuxo0buHDhAng8HubMmQMDAwNYWVkhKyuLaVNRUYH09HQMGDAAtra2XT8IilyyYcMGLFmypNU2VlZWHbq2KPGDy+XCyMiIOc7lcmFnZ9eha1J6DlR8ujEvX76Eubk5goODkZeXh/DwcCgoKGDmzJl49uwZfH19sXbtWhgaGsLc3Bzz589n+j5+/BiZmZndLsuNIln09fWhr6/fJde2tLSEoaEhYmJiGLGpqqpCSkpKuzLmKD0TmnDQjdHX10dUVBRSU1OZ5TShUAgTExMEBgaiuLgYV65cwY4dO3DhwgU4ODgwfe/cuYPS0tJuveQmj1y/fh2enp4wNjYGi8VqU1ZXfHw8Ro8eDVVVVVhbW+P48eNdHmdHKCgowO3bt1FQUACBQIDbt2/j9u3b4PF4TJuhQ4ciPDwcwOtU/vXr12P79u24dOkS7t27B29vbxgbG8PLy0tGo6DIC3Tm081RVFSEvb097O3tAYARIKFQCCUlJeY48HeSgkAgQFpaGvT19cUEidJ5ampqMGrUKCxbtgyzZ89+Z/u8vDxMnz4dq1atQmhoKGJiYrB8+XIYGRnB3d1dChG3nYCAAPz666/M36L/tuLi4jB58mQAwMOHD1FZWcm02bhxI2pqavDZZ5+hoqICEyZMQGRkJLMfjdJ7ocXkejiEEDFLnpiYGNTV1WHfvn1wdnbG9u3bZRhdz4bFYiE8PLzVp3w/Pz9ERETg/v37zLFPP/0UFRUViIyMlEKUFIpsoMtuPZw3hYfP5+PHH3/ErFmzkJiY2G1TrHsSycnJzd67ubu7030wlB4PXXbrRaioqODixYsoLCxEVlbWW50AKNKjuLi4xX0wVVVVqKurE9u7RaH0JKj49ELMzMzE3BAoFApF2tBlNwpFhhgaGrZojqqlpUVnPZQeDRUfCkWGjBs3TswcFXhdGJAuiVJ6OlR8KBQJwuPxmP0vwOtUatHeGADYtGkTvL29mfarVq3CkydPsHHjRmRnZ+PAgQM4d+4cOByOLMKnUKQGTbWmUCRIfHw83n///WbHFy9ejOPHj2PJkiXIz88X852Lj48Hh8NBVlYWTE1NsXnz5nda3lAo3R0qPhQKhUKROnTZjUKhUChSh4oPhUKhUKQOFR8KhUKhSB0qPhQKhUKROlR8KBQKhSJ1qPhQKBQKRepQ8aFQKBSK1KHiQ6FQKBSpQ8WHQqFQKFKHig+FQqFQpA4VHwqFQqFInf8Hp1SwQB4RtTcAAAAASUVORK5CYII=", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "trainer = deepxde.Trainer(problem)\n", + "trainer.compile(bst.optim.Adam(0.001), metrics=[\"l2 relative error\"]).train(iterations=10000)\n", + "trainer.saveplot(issave=True, isplot=True)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/docs/experimental_docs/unit-examples-forward/diffusion_1d.py b/docs/experimental_docs/unit-examples-forward/diffusion_1d.py new file mode 100644 index 000000000..d41538b6e --- /dev/null +++ b/docs/experimental_docs/unit-examples-forward/diffusion_1d.py @@ -0,0 +1,61 @@ +import brainstate as bst +import brainunit as u + +import deepxde.experimental as deepxde + +unit_of_x = u.meter +unit_of_t = u.second +unit_of_f = 1 / u.second + +c = 1. * u.meter ** 2 / u.second + +geom = deepxde.geometry.Interval(-1, 1) +timedomain = deepxde.geometry.TimeDomain(0, 1) +geomtime = deepxde.geometry.GeometryXTime(geom, timedomain) +geomtime = geomtime.to_dict_point(x=unit_of_x, t=unit_of_t) + + +def func(x): + y = u.math.sin(u.math.pi * x['x'] / unit_of_x) * u.math.exp(-x['t'] / unit_of_t) + return {'y': y} + + +bc = deepxde.icbc.DirichletBC(func) +ic = deepxde.icbc.IC(func) + +net = deepxde.nn.Model( + deepxde.nn.DictToArray(x=unit_of_x, t=unit_of_t), + deepxde.nn.FNN([2] + [32] * 3 + [1], "tanh"), + deepxde.nn.ArrayToDict(y=None), +) + + +def pde(x, y): + jacobian = net.jacobian(x, x='t') + hessian = net.hessian(x, xi='x', xj='x') + dy_t = jacobian["y"]["t"] + dy_xx = hessian["y"]["x"]["x"] + source = ( + u.math.exp(-x['t'] / unit_of_t) * ( + u.math.sin(u.math.pi * x['x'] / unit_of_x) - + u.math.pi ** 2 * u.math.sin(u.math.pi * x['x'] / unit_of_x) + ) + ) + return dy_t - c * dy_xx + source * unit_of_f + + +problem = deepxde.problem.TimePDE( + geomtime, + pde, + [bc, ic], + net, + num_domain=40, + num_boundary=20, + num_initial=10, + solution=func, + num_test=10000, +) + +trainer = deepxde.Trainer(problem) +trainer.compile(bst.optim.Adam(0.001), metrics=["l2 relative error"]).train(iterations=10000) +trainer.saveplot(issave=True, isplot=True) diff --git a/docs/experimental_docs/unit-examples-forward/heat.ipynb b/docs/experimental_docs/unit-examples-forward/heat.ipynb new file mode 100644 index 000000000..3728f756a --- /dev/null +++ b/docs/experimental_docs/unit-examples-forward/heat.ipynb @@ -0,0 +1,550 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Heat equation\n", + "\n", + "## Problem setup\n", + "We will solve a heat equation:\n", + "\n", + "$$\n", + "\\frac{\\partial u}{\\partial t}=\\alpha \\frac{\\partial^2u}{\\partial x^2}, \\qquad x \\in [0, 1], \\quad t \\in [0, 1]\n", + "$$\n", + "\n", + "where $alpha=0.4$ is the thermal diffusivity constant.\n", + "\n", + "With Dirichlet boundary conditions:\n", + "\n", + "$$\n", + "u(0,t) = u(1,t)=0,\n", + "$$\n", + "\n", + "and periodic(sinusoidal) inital condition:\n", + "\n", + "$$\n", + "u(x,0) = \\sin (\\frac{n\\pi x}{L}),\\qquad 0