Parsimonious Neural Networks Learn Interpretable Physical Laws

2021.04.23 Saaketh Desai, Purdue University
See table of contents below.

Machine learning methods are widely used as surrogate models in the physical sciences, but less explored is the use of machine learning to discover interpretable laws from data. This tutorial introduces parsimonious neural networks (PNNs), a combination of neural networks and evolutionary optimization to find models that balance accuracy with parsimony. As an example, you will learn how to train a PNN to learn interpretable laws that predict the melting temperature of a material given fundamental properties such as elastic constants and volume. You will also learn how to interpret the discovered PNN models as physical laws, and understand how various PNN models, as well as traditional models such as the Lindemann melting law, trade parsimony and accuracy.

Table of Contents:
00:00 Parsimonious neural networks learn interpretable physical laws
02:16 Machine learning models and their applications
04:46 Encoding neural networks for genetic algorithms
08:48 How to train a PNN?
11:35 Genetic operations on neural networks
14:21 Parsimonious neural networks – melting point
15:49 Dimensional analysis on inputs
17:25 Launching the nanoHUB tool
58:17 Discovering melting point laws
58:31 Discovering integration schemes from data