PINN for solving heat diffusivity 1D model

[mrtolzhas]

Dear Lulu,
I am trying to solve for heat diffusivity 1D model. I have 1D model (rod). I set left side to temperature 30, right side to 20. Initial temperature is 20. Also, I know temperatures at different points and time. By using those data, I want to compute heat diffusivity of the material.

Unfortunately, it is not converging. Can you please give me suggestions, what can I do?

Here is the code

import deepxde as dde
import numpy as np

from deepxde.backend import tf

C = dde.Variable(2.0)

def pde(x, y):
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 - C * dy_xx

def func(x):

initial_temperature = 20.0
left_boundary_temp = 30.0
right_boundary_temp = 20.0


left_condition = (x[:, 0:1] == 0)  
right_condition = (x[:, 0:1] == 1)  



temperature = np.full((x.shape[0], 1), initial_temperature)


temperature[left_condition] = left_boundary_temp
temperature[right_condition] = right_boundary_temp



custom_condition1 = (x[:, 1:2] == 0.2) & (x[:, 2:3] == 0.24145)
temperature[custom_condition1] = 24.061  

custom_condition2 = (x[:, 3:4] == 0.4) & (x[:, 4:5] == 0.24145)
temperature[custom_condition2] = 25.818


custom_condition3 = (x[:, 5:6] == 0.6) & (x[:, 6:7] == 0.24145)
temperature[custom_condition3] = 20.241


custom_condition4 = (x[:, 7:8] == 0.2) & (x[:, 8:9] == 0.54145)
temperature[custom_condition4] = 28.818


custom_condition5 = (x[:, 9:10] == 0.4) & (x[:, 10:11] == 0.54145)
temperature[custom_condition5] = 22.785


custom_condition6 = (x[:, 11:12] == 0.6) & (x[:, 12:13] == 0.54145)
temperature[custom_condition6] = 21.117


custom_condition7 = (x[:, 13:14] == 0.2) & (x[:, 14:15] == 0.84145)
temperature[custom_condition7] = 26.619


custom_condition8 = (x[:, 15:16] == 0.4) & (x[:, 16:17] == 0.84145)
temperature[custom_condition8] = 23.846


custom_condition9 = (x[:, 17:18] == 0.6) & (x[:, 18:9] == 0.84145)
temperature[custom_condition9] = 21.94



return temperature

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

bc = dde.DirichletBC(geomtime, func, lambda _, on_boundary: on_boundary)
ic = dde.IC(geomtime, func, lambda _, on_initial: on_initial)

observe_x = np.vstack((np.linspace(0, 1, num=10), np.full((10), 1))).T
observe_y = dde.PointSetBC(observe_x, func(observe_x), component=0)

data = dde.data.TimePDE(
geomtime,
pde,
[bc, ic, observe_y],
num_domain=40,
num_boundary=20,
num_initial=10,
anchors=observe_x,
solution=func,
num_test=10000,
)

layer_size = [2] + [32] * 3 + [1]
activation = "tanh"
initializer = "Glorot uniform"
net = dde.maps.FNN(layer_size, activation, initializer)

model = dde.Model(data, net)

model.compile(
"adam", lr=0.001, metrics=["l2 relative error"], external_trainable_variables=C
)
variable = dde.callbacks.VariableValue(C, period=1000)
losshistory, train_state = model.train(epochs=50000, callbacks=[variable])

dde.saveplot(losshistory, train_state, issave=True, isplot=True)