We consider a Preconditioned Overdamped Langevin algorithm that does not alter the invariant distribution (up to controllable discretisation errors) and ask whether preconditioning improves the standard model in terms of reducing the asymptotic variance and of accelerating convergence to equilibrium. We present a detailed study of the dependence of the asymptotic variance on preconditioning in some elementary toy models related to molecular simulation. Our theoretical results are supported by numerical simulations.
DOI: 10.5802/smai-jcm.29
CC-BY-NC-ND 4.0
@article{SMAI-JCM_2018__4__57_0,
author = {Houssam AlRachid and Letif Mones and Christoph Ortner},
title = {Some {Remarks} on {Preconditioning} {Molecular} {Dynamics}},
journal = {The SMAI Journal of computational mathematics},
pages = {57--80},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {4},
year = {2018},
doi = {10.5802/smai-jcm.29},
zbl = {1416.82020},
mrnumber = {3774648},
language = {en},
url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.29/}
}
TY - JOUR AU - Houssam AlRachid AU - Letif Mones AU - Christoph Ortner TI - Some Remarks on Preconditioning Molecular Dynamics JO - The SMAI Journal of computational mathematics PY - 2018 SP - 57 EP - 80 VL - 4 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.29/ DO - 10.5802/smai-jcm.29 LA - en ID - SMAI-JCM_2018__4__57_0 ER -
%0 Journal Article %A Houssam AlRachid %A Letif Mones %A Christoph Ortner %T Some Remarks on Preconditioning Molecular Dynamics %J The SMAI Journal of computational mathematics %D 2018 %P 57-80 %V 4 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.29/ %R 10.5802/smai-jcm.29 %G en %F SMAI-JCM_2018__4__57_0
Houssam AlRachid; Letif Mones; Christoph Ortner. Some Remarks on Preconditioning Molecular Dynamics. The SMAI Journal of computational mathematics, Volume 4 (2018), pp. 57-80. doi : 10.5802/smai-jcm.29. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.29/
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