# Discovering equations from data: symbolic regression in dynamical systems

## TL;DR

This paper reviews symbolic regression methods for discovering equations from data, compares five state-of-the-art algorithms on various dynamical systems, and identifies PySR as the most effective tool for inferring accurate equations.

## Contribution

It provides a comprehensive overview of symbolic regression techniques and benchmarks their performance, highlighting PySR's superior ability to recover governing equations.

## Key findings

- PySR outperforms other methods in recovering equations.
- Some estimates match original analytical forms closely.
- Symbolic regression shows promise for modeling real-world phenomena.

## Abstract

The process of discovering equations from data lies at the heart of physics and in many other areas of research, including mathematical ecology and epidemiology. Recently, machine learning methods known as symbolic regression emerged as a way to automate this task. This study presents an overview of the current literature on symbolic regression, while also comparing the efficiency of five state-of-the-art methods in recovering the governing equations from nine processes, including chaotic dynamics and epidemic models. Benchmark results demonstrate the PySR method as the most suitable for inferring equations, with some estimates being indistinguishable from the original analytical forms. These results highlight the potential of symbolic regression as a robust tool for inferring and modeling real-world phenomena.