Theoretical and numerical comparison of some sampling methods for molecular dynamics

¹ CERMICS, École Nationale des Ponts et Chaussées, 6-8 avenue Blaise Pascal, 77455 Marne-la-Vallée Cedex 2, France. cances@cermics.enpc.fr; legoll@cermics.enpc.fr; stoltz@cermics.enpc.fr
² INRIA, Domaine de Voluceau-Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France.
³ Institute for Mathematics and its Applications, University of Minnesota, 400 Lind Hall, 207 Church Street SE, Minneapolis MN 55455, USA.
⁴ CEA/DAM Ile-de-France, BP 12, 91680 Bruyères-le-Châtel, France.

Received: 30 July 2005

Abstract

The purpose of the present article is to compare different phase-space sampling methods, such as purely stochastic methods (Rejection method, Metropolized independence sampler, Importance Sampling), stochastically perturbed Molecular Dynamics methods (Hybrid Monte Carlo, Langevin Dynamics, Biased Random Walk), and purely deterministic methods (Nosé-Hoover chains, Nosé-Poincaré and Recursive Multiple Thermostats (RMT) methods). After recalling some theoretical convergence properties for the various methods, we provide some new convergence results for the Hybrid Monte Carlo scheme, requiring weaker (and easier to check) conditions than previously known conditions. We then turn to the numerical efficiency of the sampling schemes for a benchmark model of linear alkane molecules. In particular, the numerical distributions that are generated are compared in a systematic way, on the basis of some quantitative convergence indicators.