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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.
@article{M2AN_2007__41_2_351_0,
author = {Canc\`es, Eric and Legoll, Fr\'ed\'eric and Stoltz, Gabriel},
title = {Theoretical and numerical comparison of some sampling methods for molecular dynamics},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {351--389},
publisher = {EDP-Sciences},
volume = {41},
number = {2},
year = {2007},
doi = {10.1051/m2an:2007014},
mrnumber = {2339633},
zbl = {1138.82341},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007014/}
}
TY - JOUR AU - Cancès, Eric AU - Legoll, Frédéric AU - Stoltz, Gabriel TI - Theoretical and numerical comparison of some sampling methods for molecular dynamics JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2007 SP - 351 EP - 389 VL - 41 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007014/ DO - 10.1051/m2an:2007014 LA - en ID - M2AN_2007__41_2_351_0 ER -
%0 Journal Article %A Cancès, Eric %A Legoll, Frédéric %A Stoltz, Gabriel %T Theoretical and numerical comparison of some sampling methods for molecular dynamics %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2007 %P 351-389 %V 41 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007014/ %R 10.1051/m2an:2007014 %G en %F M2AN_2007__41_2_351_0
Cancès, Eric; Legoll, Frédéric; Stoltz, Gabriel. Theoretical and numerical comparison of some sampling methods for molecular dynamics. ESAIM: Mathematical Modelling and Numerical Analysis , Special issue on Molecular Modelling, Tome 41 (2007) no. 2, pp. 351-389. doi: 10.1051/m2an:2007014
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