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Building upon recent developments of force-based estimators with a reducedvariance for the computation of densities, radial distribution functions orlocal transport properties from molecular simulations, we show that thevariance can be further reduced by considering optimal linear combinations ofsuch estimators. This control variates approach, well known in Statistics andalready used in other branches of computational Physics, has been comparativelymuch less exploited in molecular simulations. We illustrate this idea on theradial distribution function and the one-dimensional density of a bulk andconfined Lennard-Jones fluid, where the optimal combination of estimators isdetermined for each distance or position, respectively. In addition to reducingthe variance everywhere at virtually no additional cost, this approach cures anartefact of the initial force-based estimators, namely small but non-zerovalues of the quantities in regions where they should vanish. Beyond theexamples considered here, the present work highlights more generally theunderexplored potential of control variates to estimate observables frommolecular simulations.

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