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

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.

Machine learning potentials for multicomponent systems: The Ti-Al binary system

“…Structural features play an essential role in controlling the accuracy and computational efficiency of MLPs, which are conflicting properties in general [24][25][26]. A systematic set of structural features is composed of polynomial invariants.…”

Predicting activation energies for vacancy-mediated diffusion in alloys using a transition-state cluster expansion

“…The LOOCV error of the activation energies is equivalent to 0.944 meV/atom, which is of the same order of magnitude as the error for the formation energies. This LOOCV error compares favorably to validation errors for other machine learning methods for predicting activation energies (Table S1 [35][36][37][38][39][40][41][42]), especially considering that the DFT data set contains hops in a wide variety of coordination environments, including both in the bulk and on the surface. To further validate the transition-state cluster expansion method we have used it to predict the equilibrium surface composition profile of a 4.5 nm cuboctahedral Pt3Ni nanoparticle (Pt2547Ni849) at 333 K (Figure S2, Supplementary Material section 2.1 [82]), using Metropolis Monte Carlo [83] simulations in a canonical ensemble.…”

“…However, the simplicity of these models limits their accuracy, and there is no way to systematically improve them if the predicted activation energies are not sufficiently accurate. An appealing alternative is to use systematically improvable machine-learned energy models such as cluster expansions [32][33][34] and interatomic potentials [35][36][37][38][39][40][41][42] for the rapid and accurate prediction of activation energies. As the cluster expansion is a discrete model explicitly designed to calculate the energies of local minima on the potential energy surface, it is particularly well suited for KMC.…”

Evaluation of Force Fields for Molecular Dynamics Simulations of Platinum in Bulk and Nanoparticle Forms

“…Each potential is designated by the force field type in all capital letters hyphenated with the year that it was reported, as shown in the right most column of Table 1 Other force field formulations have been proposed for platinum [104,13,61,70,72,24,29,71,26,53] and machine learning has been used recently to generate sets of force field parameters. [48,19] However, here we considered only readily available and easily implementable force fields and parameters.…”