Reduced variance analysis of molecular dynamics simulations by linear combination of estimators
Abstract
Building upon recent developments of forcebased 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 onedimensional density of a bulk and confined LennardJones 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 artifact of the initial forcebased estimators, namely, small but nonzero 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.
 Publication:

Journal of Chemical Physics
 Pub Date:
 May 2021
 DOI:
 10.1063/5.0053737
 arXiv:
 arXiv:2104.05038
 Bibcode:
 2021JChPh.154s1101C
 Keywords:

 Physics  Chemical Physics
 EPrint:
 4 Pages and 2 Figures