A perturbative approach to control variates in molecular dynamics

TL;DR

This paper introduces a perturbative variance reduction method for diffusion processes in molecular dynamics that does not require knowledge of the underlying measure, demonstrated through practical numerical examples.

Contribution

It presents a novel perturbative control variate approach applicable to complex molecular dynamics models without needing the exact measure.

Findings

Effective variance reduction in numerical experiments

Control variate constructed from simplified models

Applicable to nonequilibrium and complex systems

Abstract

We propose a general variance reduction strategy for diffusion processes. Our approach does not require the knowledge of the measure that is sampled, which may indeed be unknown as for nonequilibrium dynamics in statistical physics. We show by a perturbative argument that a control variate computed for a simplified version of the model can provide an efficient control variate for the actual problem at hand. We illustrate our method with numerical experiments and show how the control variate is built in three practical cases: the computation of the mobility of a particle in a periodic potential; the thermal flux in atom chains, relying on a harmonic approximation; and the mean length of a dimer in a solvent under shear, using a non-solvated dimer as the approximation.