Reduced variance analysis of molecular dynamics simulations by linear combination of estimators

Abstract

Building upon recent developments of force-based estimators with a reduced variance for the computation of densities, radial distribution functions or local transport properties from molecular simulations, we show that the variance can be further reduced by considering optimal linear combinations of such estimators. This control variates approach, well known in Statistics and already used in other branches of computational Physics, has been comparatively much less exploited in molecular simulations. We illustrate this idea on the radial distribution function and the one-dimensional density of a bulk and confined Lennard-Jones fluid, where the optimal combination of estimators is determined for each distance or position, respectively. In addition to reducing the variance everywhere at virtually no additional cost, this approach cures an artefact of the initial force-based estimators, namely small but non-zero values of the quantities in regions where they should vanish. Beyond the examples considered here, the present work highlights more generally the underexplored potential of control variates to estimate observables from molecular simulations.

4 Pages and 2 Figures

References in corpus (2)

• Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density
• Sampling mobility profiles of confined fluids with equilibrium molecular dynamics simulations

Cited by in corpus (10)

• Adaptive Brownian Dynamics
• Gauge Invariance of Equilibrium Statistical Mechanics
• Hyperforce balance via thermal Noether invariance of any observable
• Why hyperdensity functionals describe any equilibrium observable
• Fast quasi-centroid molecular dynamics for water and ice
• Noether invariance theory for the equilibrium force structure of soft matter
• Reduced-variance orientational distribution functions from torque sampling
• Why gauge invariance applies to statistical mechanics
• Gauge invariance and hyperforce correlation theory for equilibrium fluid mixtures
• Direct Boltzmann inversion method from particle configurations at arbitrary state points