Generalizability of Functional Forms for Interatomic Potential Models Discovered by Symbolic Regression

Generalizability of Functional Forms for Interatomic Potential Models Discovered by Symbolic Regression Alberto Hernandez and Tim Mueller ABSTRACT In recent years there has been great progress in the use of machine learning algorithms to develop interatomic potential models. Machine-learned potential models are typically orders of magnitude faster than density functional theory but also orders of magnitude slower than physics-derived models such as the embedded atom method. In our previous work, we used symbolic regression to develop fast, accurate and transferrable interatomic potential models for copper with novel functional forms that resemble those of the embedded atom method. To determine the extent to which the success of these forms was specific to copper, here we explore the generalizability of these models to other facecentered cubic transition metals and analyze their out-of-sample performance on several material properties. We found that these forms work particularly well on elements that are chemically similar to copper. When compared to optimized Sutton-Chen models, which have similar complexity, the functional forms discovered using symbolic regression perform better across all elements considered except gold where they have a similar performance. They perform similarly to a moderately more complex embedded atom form on properties on which they were trained, and they are more accurate on average on other properties. We attribute this improved generalized accuracy to the relative simplicity of the models discovered using symbolic regression. We discuss the implications of these results to the broader application of symbolic regression to the development of new potentials and highlight how models discovered for one element can be used to seed new searches for different elements. I. INTRODUCTION Researchers across several fields apply molecular dynamics and Monte Carlo simulations to advance the scientific understanding, discovery, and design of materials and molecules. Using these methods, the thermodynamic and kinetic properties of a material can be computed with knowledge of the potential energy surface. Ab initio methods such density functional theory [1] (DFT), which has demonstrated good predictive accuracy [2-4] across many chemistries and configurations of atoms, can be used to compute the potential energy surface, but the computational cost and non-linear scaling of these methods severely limits the time scale and number of atoms that can be practically modeled. Surrogate models, such as cluster expansions [5] and interatomic potential models (or force fields) [6-15], are normally orders of magnitude faster than ab initio methods and usually scale linearly with respect to system size. The improved speed and scaling of surrogate models enable atomistic simulations that inform the design of materials at larger time and length scales. Different types of interatomic potentials are commonly used for materials modeling.