In this paper, we propose an improvement of the adaptive biasing force (ABF) method, by projecting the estimated mean force onto a gradient. We show on some numerical examples that the variance of the approximated mean force is reduced using this technique, which makes the algorithm more efficient than the standard ABF method. The associated stochastic process satisfies a nonlinear stochastic differential equation. Using entropy techniques, we prove exponential convergence to the stationary state of this stochastic process.
@article{SMAI-JCM_2015__1__55_0,
author = {Alrachid, Houssam and Leli\`evre, Tony},
title = {Long-time convergence of an adaptive biasing force method: {Variance} reduction by {Helmholtz} projection},
journal = {The SMAI Journal of computational mathematics},
pages = {55--82},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {1},
year = {2015},
doi = {10.5802/smai-jcm.4},
language = {en},
url = {http://www.numdam.org/articles/10.5802/smai-jcm.4/}
}
TY - JOUR AU - Alrachid, Houssam AU - Lelièvre, Tony TI - Long-time convergence of an adaptive biasing force method: Variance reduction by Helmholtz projection JO - The SMAI Journal of computational mathematics PY - 2015 SP - 55 EP - 82 VL - 1 PB - Société de Mathématiques Appliquées et Industrielles UR - http://www.numdam.org/articles/10.5802/smai-jcm.4/ DO - 10.5802/smai-jcm.4 LA - en ID - SMAI-JCM_2015__1__55_0 ER -
%0 Journal Article %A Alrachid, Houssam %A Lelièvre, Tony %T Long-time convergence of an adaptive biasing force method: Variance reduction by Helmholtz projection %J The SMAI Journal of computational mathematics %D 2015 %P 55-82 %V 1 %I Société de Mathématiques Appliquées et Industrielles %U http://www.numdam.org/articles/10.5802/smai-jcm.4/ %R 10.5802/smai-jcm.4 %G en %F SMAI-JCM_2015__1__55_0
Alrachid, Houssam; Lelièvre, Tony. Long-time convergence of an adaptive biasing force method: Variance reduction by Helmholtz projection. The SMAI Journal of computational mathematics, Tome 1 (2015), pp. 55-82. doi : 10.5802/smai-jcm.4. http://www.numdam.org/articles/10.5802/smai-jcm.4/
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