Hello, I got this implementation of an inverse problem involving the heat equation. Can I get some help in implementing it in PhysicsNeMo?
Here is the GitHub link to my implementation:
Inverse heat equation implementation
Given the domain:
X ∈ [0, L]
t ∈ [0, 2]
We aim to recover the initial condition u(x, 0) by solving the one-dimensional heat equation:
∂u/∂t = a ∂²u/∂x², x ∈ (0, L), t > 0.
with periodic boundary conditions:
u(0, t) = u(L, t).
However, we do not directly observe u(x, 0). Instead, we have information about the solution only at a set of data points at the final time:
u(x_i, t_f) = u_exact(x_i, t_f), x_i ∈ {x_1, x_2, ..., x_N}, t_f = 2.
Our goal is to reconstruct u(x, 0) using this limited data and the structure of the heat equation.
Which I was able to implement in my code. However, it would be helpful to get some assistance in porting this code to PhysicsNeMo, as I plan to use NVIDIA PhysicsNeMo for future research projects.