Long-time convergence of an adaptive biasing force method: Variance reduction by Helmholtz projection
Alrachid, Houssam1 ; Lelièvre, Tony2
1 Ecole des Ponts ParisTech, Université Paris Est, 6-8 Avenue Blaise Pascal, Cité Descartes Marne-la-Vallée, F-77455 , France & Université Libanaise, Ecole Doctorale des Sciences et de Technologie Beyrouth, Liban
2 Ecole des Ponts ParisTech, Université Paris Est, 6-8 Avenue Blaise Pascal, Cité Descartes Marne-la-Vallée, F-77455 , France
The SMAI Journal of computational mathematics, Tome 1 (2015), pp. 55-82.

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.

Publié le :
DOI : 10.5802/smai-jcm.4
Mots clés : Adaptive biasing force; Helmholtz projection; Free energy; Variance reduction.
Alrachid, Houssam 1 ; Lelièvre, Tony 2

1 Ecole des Ponts ParisTech, Université Paris Est, 6-8 Avenue Blaise Pascal, Cité Descartes Marne-la-Vallée, F-77455 , France & Université Libanaise, Ecole Doctorale des Sciences et de Technologie Beyrouth, Liban
2 Ecole des Ponts ParisTech, Université Paris Est, 6-8 Avenue Blaise Pascal, Cité Descartes Marne-la-Vallée, F-77455 , France 
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     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},
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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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