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Issue ESAIM: Proc.
Volume 22, 2008
CANUM 2006 - Congrès National d'Analyse Numérique
Page(s) 217 - 233
DOI http://dx.doi.org/10.1051/proc:072226
Published online 01 February 2008

ESAIM: Proc., 2008, Vol. 22, pp. 217-233
DOI: 10.1051/proc:072226

Some remarks on sampling methods in Molecular Dynamics

Frédéric Legoll1, 2, Tony Lelièvre3, 2 and Gabriel Stoltz3, 2

1  LAMI, Ecole Nationale des Ponts et Chaussées, 77455 Marne-la-Vallée, France. E-mail: legoll@lami.enpc.fr
2  MICMAC, INRIA, Domaine de Voluceau-Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France.
3  CERMICS, Ecole Nationale des Ponts et Chaussées, 77455 Marne-la-Vallée, France. E-mails: lelievre@cermics.enpc.fr, stoltz@cermics.enpc.fr.


(January 12th, 2007 / Published online: 1 February 2008)

Abstract
We present an overview of sampling techniques in molecular dynamics. We start with phase-space sampling techniques, and recall that deterministic methods may suffer from non-ergodicity problems. Then, we focus on methods relying on stochastic perturbations of the usual Hamiltonian dynamics. We also consider the problem of free energy computations, where the measure to sample is supported by a submanifold which is a level set of a so-called reaction coordinate.


Résumé
Cet article présente une rapide revue des méthodes d'échantillonnage en dynamique moléculaire. On commence par présenter les méthodes d'échantillonnage de mesures définies sur tout l'espace des phases, et plus particulièrement des méthodes stochastiques fondées sur des perturbations de la dynamique hamiltonienne. En effet, les méthodes déterministes ne sont pas toujours efficaces, voire ne sont pas ergodiques. On évoque ensuite différentes manières de calculer l'énergie libre d'un système. Dans ce cas, il s'agit d'échantillonner des mesures à support sur une sous-variété, qui est la ligne de niveau de ce qu'on appelle une coordonnée de réaction.


Mathematics Subject Classification. 82B30, 37A25, 37A60, 65C30, 65C40.

Key words: Molecular dynamics, stochastic differential equations, Markov chains, ergodicity.


© EDP Sciences, ESAIM 2007


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