# Symbolic Regression in Materials Science: Discovering Interatomic Potentials from Data

arXiv: https://arxiv.org/abs/2206.06422 · HTML: https://mlsanity.com/paper/2206.06422/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 55 references that are in the map.
- First posted on arXiv 13 Jun 2022.

## Builds on (most cited first, 6 of 6)

- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Fast, accurate, and transferable many-body interatomic potentials by symbolic regression](https://mlsanity.com/paper/1904.01095/) (2019)
- [Machine Learning and Big Scientific Data](https://mlsanity.com/paper/1910.07631/) (2019)
- [Genetic programming-based learning of carbon interatomic potential for materials discovery](https://mlsanity.com/paper/2204.00735/) (2022)

## Built on by (most cited first, 3 of 3)

- [ViSymRe: Vision Multimodal Symbolic Regression](https://mlsanity.com/paper/2412.11139/) (2024)
- [Symbolic Learning for Material Discovery](https://mlsanity.com/paper/2312.11487/) (2023)
- [Symbolic regression for defect interactions in 2D materials](https://mlsanity.com/paper/2512.20785/) (2025)

## Abstract (arXiv)

Particle-based modeling of materials at atomic scale plays an important role in the development of new materials and understanding of their properties. The accuracy of particle simulations is determined by interatomic potentials, which allow to calculate the potential energy of an atomic system as a function of atomic coordinates and potentially other properties. First-principles-based ab initio potentials can reach arbitrary levels of accuracy, however their aplicability is limited by their high computational cost. Machine learning (ML) has recently emerged as an effective way to offset the high computational costs of ab initio atomic potentials by replacing expensive models with highly efficient surrogates trained on electronic structure data. Among a plethora of current methods, symbolic regression (SR) is gaining traction as a powerful "white-box" approach for discovering functional forms of interatomic potentials. This contribution discusses the role of symbolic regression in Materials Science (MS) and offers a comprehensive overview of current methodological challenges and state-of-the-art results. A genetic programming-based approach for modeling atomic potentials from raw data (consisting of snapshots of atomic positions and associated potential energy) is presented and empirically validated on ab initio electronic structure data.