Self-Healing Umbrella Sampling: Convergence and efficiency

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.

References in corpus (5)

• Escaping free-energy minima
• An efficient, multiple range random walk algorithm to calculate the density of states
• Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
• Equilibrium free energies from non-equilibrium metadynamics
• Convergence of adaptive and interacting Markov chain Monte Carlo algorithms