Long-time convergence of an adaptive biasing force method: Variance reduction by Helmholtz projection

Houssam Alrachid (1) , Tony Lelièvre (1, 2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MATHERIALS - MATHematics for MatERIALS

In this paper, we propose an improvement of the adaptive biasing force (ABF) method, by projecting the estimated mean force onto a gradient. The associated stochastic process satisfies a non linear stochastic differential equation. Using entropy techniques, we prove exponential convergence to the stationary state of this stochastic process. We finally 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.

Mots clés: Adaptive biasing force; Helmholtz projection; Free energy; Variance reduc-tion

Domaines: Analyse numérique [math.NA]

Houssam Alrachid, Tony Lelièvre. Long-time convergence of an adaptive biasing force method: Variance reduction by Helmholtz projection. SMAI Journal of Computational Mathematics, 2015, 1, pp.55 - 82. ⟨10.5802/smai-jcm.4⟩. ⟨hal-01151894⟩