Error correction in multi-fidelity molecular dynamics simulations using functional uncertainty quantification

TL;DR

This paper introduces a functional sensitivity approach using Fréchet derivatives to predict thermodynamic properties in molecular dynamics simulations across different potentials without rerunning simulations, enhancing uncertainty quantification.

Contribution

The paper presents a novel method leveraging functional derivatives to efficiently predict properties for varied interatomic potentials in MD simulations, reducing computational costs.

Findings

Accurately predicts energy and pressure for different potentials

Works under various thermodynamic conditions

Requires only first-order potential change approximation

Abstract

We use functional, Fr\'echet, derivatives to quantify how thermodynamic outputs of a molecular dynamics (MD) simulation depend on the potential used to compute atomic interactions. Our approach quantifies the sensitivity of the quantities of interest with respect to the input functions as opposed to its parameters as is done in typical uncertainty quantification methods. We show that the functional sensitivity of the average potential energy and pressure in isothermal, isochoric MD simulations using Lennard-Jones two-body interactions can be used to accurately predict those properties for other interatomic potentials (with different functional forms) without re-running the simulations. This is demonstrated under three different thermodynamic conditions, namely a crystal at room temperature, a liquid at ambient pressure, and a high pressure liquid. The method provides accurate predictions as long as the change in potential can be reasonably described to first order and does not significantly affect the region in phase space explored by the simulation. The functional uncertainty quantification approach can be used to estimate the uncertainties associated with constitutive models used in the simulation and to correct predictions if a more accurate representation becomes available.