1D Diffusion Eq

[AhmedA94]

Hello Dear Dr.lulu,

I have this code that is for 1D heat diffusion eq with homogenous domain. I want to divide the domain into two domains and assign to each domain a different value for the diffusion. Is it possible to introduce to the model an interface boundary condition to ensure a smooth transition between two domain with deepxde ?

import deepxde as dde
import numpy as np
import random

def gen_testdata():
"""Generate synthetic test data."""
t = np.linspace(0, 1, 100) # Time values from 0 to 1
x = np.linspace(0, 1, 100) # Spatial values from 0 to 1
xx, tt = np.meshgrid(x, t)
X = np.vstack((np.ravel(xx), np.ravel(tt))).T

return X

Problem parameters:

a = 1

L = 1 # Length of the bar
n = 1 # Frequency of the sinusoidal initial conditions

def pde(x, y):
"""Expresses the PDE residual of the heat equation."""
dy_t = dde.grad.jacobian(y, x, i=0, j=1)
dy_xx = dde.grad.hessian(y, x, i=0, j=0)
return dy_t - a * dy_xx

Computational geometry:

geom = dde.geometry.Interval(0, L)
timedomain = dde.geometry.TimeDomain(0, 1)
geomtime = dde.geometry.GeometryXTime(geom, timedomain)

Initial and boundary conditions:

ic = dde.IC(
geomtime, lambda x: np.zeros_like(x[:, 0:1]), lambda _, on_initial: on_initial
)

bc_left = dde.DirichletBC(geomtime, lambda x: 0, lambda x, _: np.isclose(x[0], 0))
bc_right = dde.DirichletBC(geomtime, lambda x: 1, lambda x, _: np.isclose(x[0], 1))

Define the PDE problem and configurations of the network:

data = dde.data.TimePDE(
geomtime,
pde,
[bc_left, bc_right, ic],
num_domain=2400,
num_boundary=275,
num_initial=290,
num_test=2400,
)

net = dde.nn.FNN([2] + [20] * 3 + [1], "tanh", "Glorot normal")
model = dde.Model(data, net)

Build and train the model:

model.compile("adam", lr=1e-3)
model.train(iterations=20000)
model.compile("L-BFGS")
losshistory, train_state = model.train()
model.save("trained_model.h5")

Plot/print the results

dde.saveplot(losshistory, train_state, issave=True, isplot=True)
X = gen_testdata()[0] # Get only the input features

Generate predictions and calculate mean residual

y_pred = model.predict(X)
f = model.predict(X, operator=pde)
mean_residual = np.mean(np.absolute(f))

print("Mean residual:", mean_residual)
np.savetxt("predictions.dat", np.hstack((X, y_pred))) # Save only the predictions

[lululxvi]

Yes, search Issues and Discussions, and you will find the solution.