Reducing the effect of Metropolization on mixing times in molecular dynamics simulations

TL;DR

This paper introduces a reduced-flipping generalized hybrid Monte Carlo method that minimizes momentum reversals, significantly improving the mixing times and decorrelation efficiency in molecular dynamics simulations.

Contribution

The study proposes a simple modification to GHMC algorithms that reduces momentum flipping, thereby enhancing molecular kinetics and decreasing autocorrelation times.

Findings

Reduced-flipping GHMC decreases autocorrelation times by an order of magnitude.

Momentum reversals significantly slow down system decorrelation.

The method maintains rigorous satisfaction of the balance condition.

Abstract

Molecular dynamics algorithms are subject to some amount of error dependent on the size of the time step that is used. This error can be corrected by periodically updating the system with a Metropolis criteria, where the integration step is treated as a selection probability for candidate state generation. Such a method, closely related to generalized hybrid Monte Carlo (GHMC), satisfies the balance condition by imposing a reversal of momenta upon candidate rejection. In the present study, we demonstrate that such momentum reversals can have a significant impact on molecular kinetics and extend the time required for system decorrelation, resulting in an order of magnitude increase in the integrated autocorrelation times of molecular variables for the worst cases. We present a simple method, referred to as reduced-flipping GHMC, that uses the information of the previous, current, and candidate states to reduce the probability of momentum flipping following candidate rejection while rigorously satisfying the balance condition. This method is a simple modification to traditional, automatic-flipping, GHMC methods and significantly mitigates the impact of such algorithms on molecular kinetics and simulation mixing times.