TY - JOUR
T1 - Reduced variance analysis of molecular dynamics simulations by linear combination of estimators
AU - Coles, S. W.
AU - Mangaud, E.
AU - Frenkel, D.
AU - Rotenberg, B.
N1 - Funding Information:
The authors thank Gabriel Stoltz and Tony Lelievre for useful suggestions. This project has received funding from the European Union's Horizon 2020 Research and Innovation Programme under Grant Agreement No. 766972 and from the European Research Council under the European Union's Horizon 2020 Research and Innovation Programme (Grant Agreement No. 863473). S.W.C. acknowledges the support of the Faraday Institution through the CATMAT project (Grant No. FIRG016) and the Balena High Performance Computing Service at the University of Bath.
Funding Information:
The authors thank Gabriel Stoltz and Tony Lelièvre for useful suggestions. This project has received funding from the European Union’s Horizon 2020 Research and Innovation Programme under Grant Agreement No. 766972 and from the European Research Council under the European Union’s Horizon 2020 Research and Innovation Programme (Grant Agreement No. 863473). S.W.C. acknowledges the support of the Faraday Institution through the CATMAT project (Grant No. FIRG016) and the Balena High Performance Computing Service at the University of Bath.
Publisher Copyright:
© 2021 Author(s).
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/5/21
Y1 - 2021/5/21
N2 - 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 artifact 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.
AB - 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 artifact 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.
UR - http://www.scopus.com/inward/record.url?scp=85106444474&partnerID=8YFLogxK
U2 - 10.1063/5.0053737
DO - 10.1063/5.0053737
M3 - Article
AN - SCOPUS:85106444474
SN - 0021-9606
VL - 154
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
IS - 19
M1 - 191101
ER -