A Physics-Informed Neural Network to solve 2D steady-state heat equation. Based on the methodology introduced in: Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

In this project, a PINN is trained to solve a 2D heat equation and the final results is compared to a solution based on FDM method. For more detailts about the project please read this.

The governing equation:

in the following domain:

With following boundary conditions:

Comparing PINN to FDM:

Update: Performance test on a doughnott!

Results obtained from a 9 layered DNN (1000 epochs) and FDM code on a 100×100 grid. The FDM code is written in Python, a C++ based solver could perform much better.

This implementation is based on Tensorflow 2.0 package and made possible by Google Colabratory GPU.