Physics-Informed Neural Networks: An Introduction

This repository contains several implementations of Physics-Informed Neural Networks (PINNs) using PyTorch.

Implemented methods include:

Notebook	Reference Method
PINNs_Classical.ipynb	[1]
PINNs_Galerkin.ipynb	[2]
PINNs_Ritz.ipynb	[3]

These methods are applied to solve the two-dimensional Poisson problem

$$ -\nabla^2 u = f \qquad \text{in } \Omega = (0,1)^2, $$

subject to homogeneous Dirichlet boundary conditions

$$ u = 0 \qquad \text{on } \partial\Omega. $$

Don't hesitate to contribute !