Self-healing umbrella sampling: convergence and efficiency
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The Self-Healing Umbrella Sampling (SHUS) algorithm is an adaptive biasing algorithm which has been proposed in Marsili et al. (J Phys Chem B 110(29):14011–14013, 2006) in order 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 Wang and Landau (Phys Rev E 64:056101, 2001a; Phys Rev Lett 86(10):2050–2053, 2001b). Adapting results on the convergence of the Wang-Landau algorithm obtained in Fort et al. (Math Comput 84(295):2297–2327, 2014a), 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 Barducci et al. (Phys Rev Lett 100:020,603, 2008).
KeywordsWang–Landau algorithm Stochastic approximation algorithm Free energy biasing techniques
This work is supported by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement number 614492 and by the French National Research Agency under the grants ANR-12-BS01-0019 (STAB) and ANR-14-CE23-0012 (COSMOS). We also benefited from the scientific environment of the Laboratoire International Associé between the Centre National de la Recherche Scientifique and the University of Illinois at Urbana-Champaign.
- Fort, G.: Central limit theorems for stochastic approximation with controlled Markov chain dynamics. ESAIM: Probab. Stat. 19, 60–80 (2015)Google Scholar
- Fort, G., Jourdain, B., Kuhn, E., Lelièvre, T., Stoltz, G.: Convergence of the Wang-Landau. Math. Comput. 84(295), 2297–2327 (2014a)Google Scholar
- Fort, G., Jourdain, B., Kuhn, E., Lelièvre, T., Stoltz, G.: Efficiency of the Wang-Landau algorithm: a simple test case. Appl. Math. Res. Express 2014(2), 275–311 (2014b)Google Scholar
- Marsili, S., Barducci, A., Chelli, R., Procacci, P., Schettino, V.: Self-healing umbrella sampling: a non-equilibrium approach for quantitative free energy calculations. J. Phys. Chem. B 110(29), 14011–14013 (2006)Google Scholar
- Mengersen, K., Robert, C.: IID sampling with self-avoiding particle filters: the pinball sampler. In: Bernardo, J., David, A., Berger, J., West, M. (eds.) Bayesian Statistics 7 (2003)Google Scholar
- Wang, F., Landau, D.: Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram. Phys. Rev. E 64, 056101 (2001a)Google Scholar
- Wang, F.G., Landau, D.P.: Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett. 86(10), 2050–2053 (2001b)Google Scholar