# Symbolic Regression in Materials Science

## TL;DR

This paper explores the application of symbolic regression, especially genetic programming-based methods, in materials science for discovering analytical models and functional forms, demonstrating its potential as an alternative to traditional machine learning approaches.

## Contribution

It introduces the use of GPSR in materials science, presents two case studies, and advocates for its broader adoption in the field as a powerful analytical tool.

## Key findings

- GPSR successfully derived the JMAK transformation law.
- GPSR learned the Landau free energy functional for a phase transition.
- Symbolic regression offers an interpretable alternative to black-box models.

## Abstract

We showcase the potential of symbolic regression as an analytic method for use in materials research. First, we briefly describe the current state-of-the-art method, genetic programming-based symbolic regression (GPSR), and recent advances in symbolic regression techniques. Next, we discuss industrial applications of symbolic regression and its potential applications in materials science. We then present two GPSR use-cases: formulating a transformation kinetics law and showing the learning scheme discovers the well-known Johnson-Mehl-Avrami-Kolmogorov (JMAK) form, and learning the Landau free energy functional form for the displacive tilt transition in perovskite LaNiO$_3$. Finally, we propose that symbolic regression techniques should be considered by materials scientists as an alternative to other machine-learning-based regression models for learning from data.