This tutorial gives a short introduction to PINNs and shows how to implement in Pytorch a PINN to model a growth function and a 1-dimensional wave.

For this tutorial I mainly credit the original paper [1], the official Github repository [2], and these great posts [4, 5], which introduce the PINNs from a machine learning and a physics perspective, respectively.

[1] Raissi, Maziar, Paris Perdikaris, and George E. Karniadakis. "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations." Journal of Computational physics 378 (2019): 686-707.

[2] Raissi, Maziar, Paris Perdikaris, and George E. Karniadakis. "Physics Informed Deep Learning".

[3] Nascimento, R. G., Fricke, K., & Viana, F. A. (2020). A tutorial on solving ordinary differential equations using Python and hybrid physics-informed neural network. Engineering Applications of Artificial Intelligence, 96, 103996.

[4] Dagrada, Dario. "Introduction to Physics-informed Neural Networks" (code).

[5] Paialunga Piero. "Physics and Artificial Intelligence: Introduction to Physics Informed Neural Networks".

[6] "Physics-Informed-Neural-Networks (PINNs)" - implementation of PINNs in TensorFlow 2 and PyTorch for the Burgers' and Helmholtz PDE.