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

TL;DR

This paper introduces a symbolic regression-based machine learning algorithm that discovers simple, accurate, and computationally efficient many-body interatomic potentials, capable of generalizing well across different material properties and scales.

Contribution

The authors develop a novel symbolic regression method that finds physically interpretable interatomic potentials with high transferability and efficiency, improving upon existing machine learning approaches.

Findings

Successfully rediscovered known potentials like Lennard-Jones and Sutton Chen.

Generated accurate copper potentials from density functional theory data.

Achieved models as fast as embedded atom models with good transferability.

Abstract

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.