Update docs

Author: lululxvi

docs/demos/forward.rst

@@ -3,32 +3,55 @@ Demos of Forward Problems
 
 Here are some demos of solving forward problems of PDEs.
 
+ODEs
+----
+
+- `ODE system <https://github.com/lululxvi/deepxde/blob/master/examples/ode_system.py>`_
+- `Lotka-Volterra equation <https://github.com/lululxvi/deepxde/blob/master/examples/Lotka_Volterra_Colab.ipynb>`_
+
+Time-independent PDEs
+---------------------
+
 .. toctree::
    :maxdepth: 1
 
    poisson.1d.dirichlet
-   burgers
 
-- `Beltrami flow <https://github.com/lululxvi/deepxde/blob/master/examples/Beltrami_flow.py>`_
-- `Burgers equation with residual-based adaptive refinement (RAR) <https://github.com/lululxvi/deepxde/blob/master/examples/Burgers_RAR.py>`_
-- `Euler beam <https://github.com/lululxvi/deepxde/blob/master/examples/Euler_beam.py>`_
-- `Kovasznay flow <https://github.com/lululxvi/deepxde/blob/master/examples/Kovasznay_flow.py>`_
-- `Laplace equation on a disk <https://github.com/lululxvi/deepxde/blob/master/examples/Laplace_disk.py>`_
-- `Lotka-Volterra equation <https://github.com/lululxvi/deepxde/blob/master/examples/Lotka_Volterra_Colab.ipynb>`_
-- `Poisson equation over an L-shaped domain <https://github.com/lululxvi/deepxde/blob/master/examples/Poisson_Lshape.py>`_
 - `Poisson equation in 1D with Dirichlet/Neumann boundary conditions <https://github.com/lululxvi/deepxde/blob/master/examples/Poisson_Neumann_1d.py>`_
 - `Poisson equation in 1D with Dirichlet/Robin boundary conditions <https://github.com/lululxvi/deepxde/blob/master/examples/Poisson_Robin_1d.py>`_
 - `Poisson equation in 1D with the multi-scale Fourier feature architecture <https://github.com/lululxvi/deepxde/blob/master/examples/Poisson_multiscale_1d.py>`_
 - `Poisson equation in 1D with Dirichlet/periodic boundary conditions <https://github.com/lululxvi/deepxde/blob/master/examples/Poisson_periodic_1d.py>`_
-- `Volterra IDE <https://github.com/lululxvi/deepxde/blob/master/examples/Volterra_IDE.py>`_
+- `Poisson equation over an L-shaped domain <https://github.com/lululxvi/deepxde/blob/master/examples/Poisson_Lshape.py>`_
+- `Laplace equation on a disk <https://github.com/lululxvi/deepxde/blob/master/examples/Laplace_disk.py>`_
+- `Euler beam <https://github.com/lululxvi/deepxde/blob/master/examples/Euler_beam.py>`_
+
+Time-dependent PDEs
+-------------------
+
+.. toctree::
+   :maxdepth: 1
+
+   burgers
+
 - `Diffusion equation <https://github.com/lululxvi/deepxde/blob/master/examples/diffusion_1d.py>`_
 - `Diffusion equation with hard initial and boundary conditions <https://github.com/lululxvi/deepxde/blob/master/examples/diffusion_1d_exactBC.py>`_
 - `Diffusion equation with training points resampling <https://github.com/lululxvi/deepxde/blob/master/examples/diffusion_1d_resample.py>`_
+- `Heat equation <https://github.com/lululxvi/deepxde/blob/master/examples/heat_conduction_1d_uniform_bar.ipynb>`_
+- `Burgers equation with residual-based adaptive refinement (RAR) <https://github.com/lululxvi/deepxde/blob/master/examples/Burgers_RAR.py>`_
+- `Beltrami flow <https://github.com/lululxvi/deepxde/blob/master/examples/Beltrami_flow.py>`_
+- `Kovasznay flow <https://github.com/lululxvi/deepxde/blob/master/examples/Kovasznay_flow.py>`_
+- `Wave propagation with spatio-temporal multi-scale Fourier feature architecture <https://github.com/lululxvi/deepxde/blob/master/examples/wave_1d.py>`_
+
+Integro-differential equations
+------------------------------
+
+- `Integro-differential equation <https://github.com/lululxvi/deepxde/blob/master/examples/ide.py>`_
+- `Volterra IDE <https://github.com/lululxvi/deepxde/blob/master/examples/Volterra_IDE.py>`_
+
+fractional PDEs
+---------------
+
 - `fractional Poisson equation in 1D <https://github.com/lululxvi/deepxde/blob/master/examples/fractional_Poisson_1d.py>`_
 - `fractional Poisson equation in 2D <https://github.com/lululxvi/deepxde/blob/master/examples/fractional_Poisson_2d.py>`_
 - `fractional Poisson equation in 3D <https://github.com/lululxvi/deepxde/blob/master/examples/fractional_Poisson_3d.py>`_
 - `fractional diffusion equation <https://github.com/lululxvi/deepxde/blob/master/examples/fractional_diffusion_1d.py>`_
-- `Heat equation <https://github.com/lululxvi/deepxde/blob/master/examples/heat_conduction_1d_uniform_bar.ipynb>`_
-- `Integro-differential equation <https://github.com/lululxvi/deepxde/blob/master/examples/ide.py>`_
-- `ODE system <https://github.com/lululxvi/deepxde/blob/master/examples/ode_system.py>`_
-- `Wave propagation with spatio-temporal multi-scale Fourier feature architecture <https://github.com/lululxvi/deepxde/blob/master/examples/wave_1d.py>`_

docs/demos/func.rst

@@ -3,8 +3,19 @@ Demos of Function Approximation
 
 Here are some demos of learning functions.
 
+Function approximation
+----------------------
+
 - `Learning a function from a dataset <https://github.com/lululxvi/deepxde/blob/master/examples/dataset.py>`_
 - `Learning a function from the formula <https://github.com/lululxvi/deepxde/blob/master/examples/func.py>`_
+
+Uncertainty quantification
+--------------------------
+
 - `Learning a function with uncertainty quantification <https://github.com/lululxvi/deepxde/blob/master/examples/func_uncertainty.py>`_
-- `Multi-fidelity learning from a dataset <https://github.com/lululxvi/deepxde/blob/master/examples/mf_dataset.py>`_
+
+Multi-fidelity learning
+-----------------------
+
 - `Multi-fidelity learning from the formulas <https://github.com/lululxvi/deepxde/blob/master/examples/mf_func.py>`_
+- `Multi-fidelity learning from a dataset <https://github.com/lululxvi/deepxde/blob/master/examples/mf_dataset.py>`_

docs/demos/inverse.rst

@@ -3,14 +3,25 @@ Demos of Inverse Problems
 
 Here are some demos of solving inverse problems of PDEs.
 
+ODEs
+----
+
 .. toctree::
    :maxdepth: 1
 
    lorenz.inverse
-   
+
 - `Inverse problem for the Lorenz system with exogenous input <https://github.com/lululxvi/deepxde/blob/master/examples/Lorenz_inverse_forced_Colab.ipynb>`_
+
+PDEs
+----
+   
 - `Inverse problem for the diffusion equation <https://github.com/lululxvi/deepxde/blob/master/examples/diffusion_1d_inverse.py>`_
+- `Inverse Problem for the diffusion-reaction system <https://github.com/lululxvi/deepxde/blob/master/examples/reaction_inverse.py>`_
 - `Inverse problem for the Poisson equation with unknown forcing field <https://github.com/lululxvi/deepxde/blob/master/examples/elliptic_inverse_field.py>`_
+
+fractional PDEs
+---------------
+
 - `Inverse problem for the fractional Poisson equation in 1D <https://github.com/lululxvi/deepxde/blob/master/examples/fractional_Poisson_1d_inverse.py>`_
 - `Inverse problem for the fractional Poisson equation in 2D <https://github.com/lululxvi/deepxde/blob/master/examples/fractional_Poisson_2d_inverse.py>`_
-- `Inverse Problem for the diffusion-reaction system <https://github.com/lululxvi/deepxde/blob/master/examples/reaction_inverse.py>`_