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

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 many-body 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.

Accelerated prediction of atomically precise cluster structures using on-the-fly machine learning

The chemical and structural properties of atomically precise nanoclusters are of great interest in numerous applications,but predicting the stable structures of clusters can be computationally expensive.In this work,we present a procedure for rapidly predicting low-energy structures of nanoclusters by combining a genetic algorithm with interatomic potentials actively learned on-the-fly.Applying this approach to aluminum clusters with 21 to 55 atoms,we have identified structures with lower energy than any reported in the literature for 25 out of the 35 sizes.Our benchmarks indicate that the active learning procedure accelerated the average search speed by about an order of magnitude relative to genetic algorithm searches using only density functional calculations.This work demonstrates a feasible way to systematically discover stable structures for large nanoclusters and provides insights into the transferability of machine-learned interatomic potentials for nanoclusters.