Mathematical understanding of detailed balance condition violation and its application to Langevin dynamics

TL;DR

This paper introduces a modified Langevin dynamics method that violates detailed balance to improve sampling efficiency, achieving faster convergence and reduced correlation times compared to traditional methods.

Contribution

It provides a theoretical framework for understanding detailed balance violation and applies it to Langevin dynamics to enhance sampling performance.

Findings

Accelerated relaxation to target distribution

Reduced correlation time in steady state

Effective implementation of non-detailed balance Langevin dynamics

Abstract

We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined distribution such as the Gibbs-Boltzmann one is performed under the detailed balance condition. In the present study, we propose a modified Langevin dynamics violating the detailed balance condition on the transition-probability formulation. We confirm that the numerical implementation of the proposed method actually demonstrates two major beneficial improvements: acceleration of the relaxation to the predetermined distribution and reduction of the correlation time between two different realizations in the steady state.