Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations

TL;DR

This paper presents a variational algorithm to efficiently estimate the likelihood of rare events in nonequilibrium molecular dynamics by optimizing control forces, improving sampling efficiency and accuracy.

Contribution

It introduces a novel variational method with explicit gradient forms for estimating large deviation functions in nonequilibrium systems, including correction expressions and benchmarking.

Findings

High accuracy of variational estimates in benchmark models

Significant efficiency gains over traditional Monte Carlo methods

Effective handling of dynamical phase transitions

Abstract

We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis is made possible by explicit forms for the gradients of a cost function in terms of the susceptibility of driven trajectories to changes in variational parameters. We consider probabilities of time-integrated dynamical observables as characterized by their large deviation functions, and find that in many cases the variational estimate is quantitatively accurate. Additionally, we provide expressions to exactly correct the variational estimate that can be evaluated directly. We benchmark this algorithm against the numerically exact solution of a model of a driven particle in a periodic potential, where the control force can be represented with a complete basis. We then demonstrate the utility of the algorithm in a model of repulsive particles on a line, which undergo a dynamical phase transition, resulting in singular changes to the form of the optimal control force. In both systems, we find fast convergence and are able to evaluate large deviation functions with significant increases in statistical efficiency over alternative Monte Carlo approaches.