Can you make a neural network satisfy a physical law? There are two main types of these laws: symmetries and ordinary/partial differential equations. This tutorial will focus on differential equations. The simplest way to bake information about a differential equation with neural networks is to create a regularization term for the loss function used in training. First example in this tutorial will explain the mathematics of this idea. Next, this tutorial will cover applying physics-informed neural networks to obtain simulator free solution for forward model evaluations; using a simple example from solid mechanics. All these ideas are implemented in PyTorch. This tutorial assumes some familiarity with how conventional neural networks are trained (stochastic gradient descent). Also, you need to know the basics of PyTorch to follow along. Going over this tutorial should be sufficient: https://pytorch.org/tutorials/beginner/pytorch_with_examples.html.

Researchers should cite this work as follows:

• Atharva Hans, Ilias Bilionis (2021), "A Hands-on Introduction to Physics-Informed Neural Networks," https://nanohub.org/resources/handsonpinns. (DOI: 10.21981/FN6Y-NC12).

  BibTex | EndNote

1. data-driven materials discovery
2. data science
3. machine learning
4. materials science
5. NCN Group - Machine Learning Hands-on
6. neural networks
7. ODEs
8. PDEs
9. physics-based machine learning
10. Physics-Informed Neural Networks notebook
11. PyTorch