PINN model with exogeneous inputs (parameters) simulated at varyed initial conditions

[John-Silva-29]

Hi everyone,
I am trying to simulate a ode system that has a parameter. Moreover, i want to fit a PINN that fits the model at different initial conditions. The final goal is to use in a process control framework. But i am getting errors related to data diensions. Below is the code and the error. Can someone help me please?

import torch as torch
import os
os.environ["DDE_BACKEND"] = "pytorch" # Set backend to PyTorch
import deepxde as dde #type: ignore
import numpy as np

-----------------------------

1. Define the ODE system

-----------------------------

def ode_system(inputs, y):
t = inputs[:, 0:1]
mu = inputs[:, 1:2]
y1_0 = inputs[:, 2:3]
y2_0 = inputs[:, 3:4]

y1 = y[:, 0:1]
y2 = y[:, 1:2]

dy1_dt = dde.grad.jacobian(y, inputs, i=0, j=0)
dy2_dt = dde.grad.jacobian(y, inputs, i=1, j=0)

f1 = dy1_dt - y2
f2 = dy2_dt + mu * y2 + y1

return [f1, f2]

-----------------------------

2. Geometry [t, mu, y1_0, y2_0]

-----------------------------

geom = dde.geometry.Rectangle(
[0.0, 0.1, 0.5, -1.0],
[10.0, 1.0, 2.0, 1.0]
)

-----------------------------

3. Unified initial condition residuals

-----------------------------

def ic_residuals(inputs, outputs):
r1 = outputs[:, 0:1] - inputs[:, 2:3] # y1 - y1_0
r2 = outputs[:, 1:2] - inputs[:, 3:4] # y2 - y2_0
print(r1.size)
print(r2.size)
return r1, r2

-----------------------------

4. Boundary condition: only where t=0

-----------------------------

def boundary(x, on_boundary):
return on_boundary and np.isclose(x[0], 0.0)

bc1 = dde.icbc.OperatorBC(
geom,
lambda x, y, _: ic_residuals(x, y)[0],
boundary,
)

bc2 = dde.icbc.OperatorBC(
geom,
lambda x, y, _: ic_residuals(x, y)[1],
boundary,
)

-----------------------------

5. Data

-----------------------------

data = dde.data.PDE(
geom,
ode_system,
[bc1, bc2],
num_domain=500,
num_boundary=50,
num_test=100
)

-----------------------------

6. Network

-----------------------------

net = dde.nn.FNN([4] + [64] * 3 + [2], "tanh", "Glorot normal")

-----------------------------

7. Model

-----------------------------

model = dde.Model(data, net)
model.compile("adam", lr=0.001)
model.train(iterations=5000)

Traceback (most recent call last):
File "C:\Users\jonil\Desktop\PINN\deepxde-master\deepxde-master\examples\pinn_forward\ex1.py", line 66, in
data = dde.data.PDE(
^^^^^^^^^^^^^
File "C:\Users\jonil\Desktop\PINN\venv_dde\Lib\site-packages\deepxde\data\pde.py", line 135, in init
self.train_next_batch()
File "C:\Users\jonil\Desktop\PINN\venv_dde\Lib\site-packages\deepxde\utils\internal.py", line 39, in wrapper
return func(self, *args, **kwargs)
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "C:\Users\jonil\Desktop\PINN\venv_dde\Lib\site-packages\deepxde\data\pde.py", line 199, in train_next_batch
self.train_x_all = self.train_points()
^^^^^^^^^^^^^^^^^^^
File "C:\Users\jonil\Desktop\PINN\venv_dde\Lib\site-packages\deepxde\utils\internal.py", line 39, in wrapper
return func(self, *args, **kwargs)
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "C:\Users\jonil\Desktop\PINN\venv_dde\Lib\site-packages\deepxde\data\pde.py", line 298, in train_points
X = np.vstack((tmp, X))
^^^^^^^^^^^^^^^^^^^
File "C:\Users\jonil\Desktop\PINN\venv_dde\Lib\site-packages\numpy\core\shape_base.py", line 289, in vstack
return _nx.concatenate(arrs, 0, dtype=dtype, casting=casting)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
ValueError: all the input array dimensions except for the concatenation axis must match exactly, but along dimension 1, the array at index 0 has size 2 and the array at index 1 has size 4