# Fast, accurate, and transferable many-body interatomic potentials by symbolic regression

arXiv: https://arxiv.org/abs/1904.01095 · HTML: https://mlsanity.com/paper/1904.01095/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2019.

## Built on by (most cited first, 23 of 23)

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- [Interpretable Analytic Calabi-Yau Metrics via Symbolic Distillation](https://mlsanity.com/paper/2602.07834/) (2026)
- [Generalizability of Functional Forms for Interatomic Potential Models Discovered by Symbolic Regression](https://mlsanity.com/paper/2210.15124/) (2022)
- [Interpretable Ensemble Learning for Materials Property Prediction with Classical Interatomic Potentials: Carbon as an Example](https://mlsanity.com/paper/2308.10818/) (2023)
- [Exploring Multi-view Symbolic Regression methods in physical sciences](https://mlsanity.com/paper/2509.10500/) (2025)
- [Symbolic regression for defect interactions in 2D materials](https://mlsanity.com/paper/2512.20785/) (2025)

## Abstract (arXiv)

The length and time scales of atomistic simulations are limited by the computational cost of the methods used to predict material properties. In recent years there has been great progress in the use of machine learning algorithms to develop fast and accurate interatomic potential models, but it remains a challenge to develop models that generalize well and are fast enough to be used at extreme time and length scales. To address this challenge, we have developed a machine learning algorithm based on symbolic regression in the form of genetic programming that is capable of discovering accurate, computationally efficient manybody potential models. The key to our approach is to explore a hypothesis space of models based on fundamental physical principles and select models within this hypothesis space based on their accuracy, speed, and simplicity. The focus on simplicity reduces the risk of overfitting the training data and increases the chances of discovering a model that generalizes well. Our algorithm was validated by rediscovering an exact Lennard-Jones potential and a Sutton Chen embedded atom method potential from training data generated using these models. By using training data generated from density functional theory calculations, we found potential models for elemental copper that are simple, as fast as embedded atom models, and capable of accurately predicting properties outside of their training set. Our approach requires relatively small sets of training data, making it possible to generate training data using highly accurate methods at a reasonable computational cost. We present our approach, the forms of the discovered models, and assessments of their transferability, accuracy and speed.