# Introduction to Symbolic Regression in the Physical Sciences

arXiv: https://arxiv.org/abs/2512.15920 · HTML: https://mlsanity.com/paper/2512.15920/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 12 references that are in the map.
- First posted on arXiv 17 Dec 2025.

## Builds on (most cited first, 3 of 3)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl](https://mlsanity.com/paper/2305.01582/) (2023)

## Built on by (most cited first, 2 of 2)

- [DeepInflation: an AI agent for research and model discovery of inflation](https://mlsanity.com/paper/2601.14288/) (2026)
- [How AI Agents Discover Scientific Equations: From Hydrotope Rediscovery to New Water-Wave Amplitudes](https://mlsanity.com/paper/2610.00435/) (2026)

## Abstract (arXiv)

Symbolic regression (SR) has emerged as a powerful method for uncovering interpretable mathematical relationships from data, offering a novel route to both scientific discovery and efficient empirical modelling. This article introduces the Special Issue on Symbolic Regression for the Physical Sciences, motivated by the Royal Society discussion meeting held in April 2025. The contributions collected here span applications from automated equation discovery and emergent-phenomena modelling to the construction of compact emulators for computationally expensive simulations. The introductory review outlines the conceptual foundations of SR, contrasts it with conventional regression approaches, and surveys its main use cases in the physical sciences, including the derivation of effective theories, empirical functional forms and surrogate models. We summarise methodological considerations such as search-space design, operator selection, complexity control, feature selection, and integration with modern AI approaches. We also highlight ongoing challenges, including scalability, robustness to noise, overfitting and computational complexity. Finally we emphasise emerging directions, particularly the incorporation of symmetry constraints, asymptotic behaviour and other theoretical information. Taken together, the papers in this Special Issue illustrate the accelerating progress of SR and its growing relevance across the physical sciences.