Self-Healing Umbrella Sampling: Convergence and efficiency

Gersende Fort 1 Benjamin Jourdain 2, 3 Tony Lelièvre 2, 4 Gabriel Stoltz 2, 4
3 MATHRISK - Mathematical Risk handling
Inria Paris-Rocquencourt, UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech
4 MATHERIALS - MATHematics for MatERIALS
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : The Self-Healing Umbrella Sampling (SHUS) algorithm is an adaptive biasing algorithm which has been proposed to efficiently sample a multimodal probability measure. We show that this method can be seen as a variant of the well-known Wang-Landau algorithm. Adapting results on the convergence of the Wang-Landau algorithm, we prove the convergence of the SHUS algorithm. We also compare the two methods in terms of efficiency. We finally propose a modification of the SHUS algorithm in order to increase its efficiency, and exhibit some similarities of SHUS with the well-tempered metadynamics method.
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https://hal.archives-ouvertes.fr/hal-01073201
Contributor : Gabriel Stoltz <>
Submitted on : Thursday, October 9, 2014 - 11:08:24 AM
Last modification on : Friday, June 7, 2019 - 11:18:36 AM

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Gersende Fort, Benjamin Jourdain, Tony Lelièvre, Gabriel Stoltz. Self-Healing Umbrella Sampling: Convergence and efficiency. Statistics and Computing, Springer Verlag (Germany), 2017, 27 (1), pp.147-168. ⟨10.1007/s11222-015-9613-2⟩. ⟨hal-01073201⟩

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