Dynamical traps in Wang-Landau sampling of continuous systems: Mechanism and solution

TL;DR

This paper investigates the causes of dynamical trapping in Wang-Landau sampling of continuous systems, revealing the mechanism and proposing an inter-swapping solution to improve sampling efficiency.

Contribution

It identifies the trapping mechanism in Wang-Landau sampling and introduces a simple, effective inter-swapping method to prevent it, enhancing sampling accuracy.

Findings

Trapping occurs near local energy extrema, disrupting density-of-states estimation.

Inter-swapping configurations between multiple trajectories prevents trapping.

The proposed method significantly improves sampling efficiency.

Abstract

We study the mechanism behind dynamical trappings experienced during Wang-Landau sampling of continuous systems reported by several authors. Trapping is caused by the random walker coming close to a local energy extremum, although the mechanism is different from that of critical slowing down encountered in conventional molecular dynamics or Monte Carlo simulations. When trapped, the random walker misses entire or even several stages of Wang-Landau modification factor reduction, leading to inadequate sampling of configuration space and a rough density-of-states even though the modification factor has been reduced to very small values. Trapping is dependent on specific systems, the choice of energy bins, and Monte Carlo step size, making it highly unpredictable. A general, simple, and effective solution is proposed where the configurations of multiple parallel Wang-Landau trajectories are inter-swapped to prevent trapping. We also explain why swapping frees the random walker from such traps. The efficacy of the proposed algorithm is demonstrated.