Theoretical and numerical comparison of some sampling methods for molecular dynamics

Eric Cancès; Frédéric Legoll; Gabriel Stoltz

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 2, page 351-389
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Cancès, Eric, Legoll, Frédéric, and Stoltz, Gabriel. "Theoretical and numerical comparison of some sampling methods for molecular dynamics." ESAIM: Mathematical Modelling and Numerical Analysis 41.2 (2007): 351-389. <http://eudml.org/doc/250084>.

@article{Cancès2007,
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. },
author = {Cancès, Eric, Legoll, Frédéric, Stoltz, Gabriel},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Sampling methods; canonical ensemble; Molecular Dynamics.},
language = {eng},
month = {6},
number = {2},
pages = {351-389},
publisher = {EDP Sciences},
title = {Theoretical and numerical comparison of some sampling methods for molecular dynamics},
url = {http://eudml.org/doc/250084},
volume = {41},
year = {2007},
}

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
DA - 2007/6//
PB - EDP Sciences
VL - 41
IS - 2
SP - 351
EP - 389
AB - 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.
LA - eng
KW - Sampling methods; canonical ensemble; Molecular Dynamics.
UR - http://eudml.org/doc/250084
ER -

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