Self-Healing Umbrella Sampling: Convergence and efficiency

TL;DR

The paper analyzes the convergence and efficiency of the Self-Healing Umbrella Sampling (SHUS) algorithm, a variant of Wang-Landau, proposing modifications to enhance its performance and comparing it with well-tempered metadynamics.

Contribution

It proves the convergence of SHUS, relates it to Wang-Landau, and introduces modifications to improve its efficiency and similarities with metadynamics.

Findings

SHUS converges under certain conditions.

Modified SHUS shows increased efficiency.

SHUS shares features with well-tempered metadynamics.

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.