Uncertainty Quantification in Atomistic Simulations of Silicon using Interatomic Potentials

Abstract

Atomistic simulations often rely on interatomic potentials to access greater time- and length- scales than those accessible to first principles methods such as density functional theory (DFT). However, since a parameterised potential typically cannot reproduce the true potential energy surface of a given system, we should expect a decrease in accuracy and increase in error in quantities of interest calculated from simulations. Quantifying the uncertainty on the outputs of atomistic simulations is thus an important, necessary step so that there is confidence in results and available metrics to explore improvements in said simulations. Here, we address this research question by forming ensembles of Atomic Cluster Expansion (ACE) potentials, and using Conformal Prediction with DFT training data to provide meaningful, calibrated error bars on several quantities of interest for silicon: the bulk modulus, elastic constants, relaxed vacancy formation energy, and the vacancy migration barrier. We evaluate the effects on uncertainty bounds using a range of different potentials and training sets.