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Title: A comparison of generalized hybrid Monte Carlo methods with and without momentum flip

Abstract

The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC.

Authors:
 [1];  [2];  [3]
  1. Fujitsu Laboratories of Europe Ltd (FLE), Hayes Park Central, Hayes End Road, Hayes UB4 8FE (United Kingdom)
  2. Department of Mathematics, Freie Universitaet Berlin, Arnimallee 2-6, 14195 Berlin (Germany)
  3. Universitaet Potsdam, Institut fuer Mathematik, Am Neuen Palais 10, D-14469 Potsdam (Germany)
Publication Date:
OSTI Identifier:
21167770
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 228; Journal Issue: 6; Other Information: DOI: 10.1016/j.jcp.2008.12.014; PII: S0021-9991(08)00632-3; Copyright (c) 2008 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BALANCES; COMPARATIVE EVALUATIONS; EFFICIENCY; FUNCTIONS; MODIFICATIONS; MOLECULAR DYNAMICS METHOD; MONTE CARLO METHOD; RANDOMNESS; SIMULATION; STOCHASTIC PROCESSES; THERMOSTATS

Citation Formats

Akhmatskaya, Elena, Bou-Rabee, Nawaf, and Reich, Sebastian. A comparison of generalized hybrid Monte Carlo methods with and without momentum flip. United States: N. p., 2009. Web. doi:10.1016/j.jcp.2008.12.014.
Akhmatskaya, Elena, Bou-Rabee, Nawaf, & Reich, Sebastian. A comparison of generalized hybrid Monte Carlo methods with and without momentum flip. United States. https://doi.org/10.1016/j.jcp.2008.12.014
Akhmatskaya, Elena, Bou-Rabee, Nawaf, and Reich, Sebastian. 2009. "A comparison of generalized hybrid Monte Carlo methods with and without momentum flip". United States. https://doi.org/10.1016/j.jcp.2008.12.014.
@article{osti_21167770,
title = {A comparison of generalized hybrid Monte Carlo methods with and without momentum flip},
author = {Akhmatskaya, Elena and Bou-Rabee, Nawaf and Reich, Sebastian},
abstractNote = {The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC.},
doi = {10.1016/j.jcp.2008.12.014},
url = {https://www.osti.gov/biblio/21167770}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = 6,
volume = 228,
place = {United States},
year = {Wed Apr 01 00:00:00 EDT 2009},
month = {Wed Apr 01 00:00:00 EDT 2009}
}