Abstract

Interatomic potentials (IPs) approximate the potential energy surface of systems of atoms as a function of their positions and are seen as a computationally feasible alternative to electronic structure calculations, which additionally model the motion of electrons around atomic nuclei. IPs form a basis of molecular mechanics and molecular dynamics simulations in computational chemistry, computational physics and computational materials science and have proven useful in explaining and predicting materials properties, such as lattice parameters, surface energies, interfacial energies, adsorption, cohesion, thermal expansion, and elastic and plastic material behaviour, as well as chemical reactions. Empirical IPs have between 2 and 11 parameters, rising to >1000 parameters for modern machine-learning potentials, and the highly nonlinear and nonconvex nature of the overall model necessitates quantifying the uncertainty in their choice and how this propagates to quantities of interest, such as mechanical or chemical properties of materials. Usually, this is achieved by employing a Bayesian approach, whereby one assumes some prior probability distribution for the parameters defining a given interatomic potential, which are subsequently updated using available data originating from experiments or higher-level theories. In this talk I will discuss ongoing work on advancing the mathematical understanding of how uncertainty quantification for IPs should be conducted. In particular, I will discuss (i) how the vast literature on the topic of continuum stochastic elasticity can be leveraged to provide an information-theoretic approach to deriving prior distributions for the IP parameters ; (ii) how polynomial approximation theory can be leveraged to reduce the uncertainty.