Variance-reduced random batch Langevin dynamics

TL;DR

This paper introduces a variance-reduction technique for random batch Langevin dynamics that effectively minimizes artificial heating, improves accuracy with smaller batch sizes, and aligns with fluctuation-dissipation principles.

Contribution

It develops a novel variance-reduction approach for random batch Langevin dynamics, addressing artificial heating and ensuring theoretical consistency.

Findings

Significant variance reduction achieved with smaller batch sizes

Method aligns with fluctuation-dissipation theorem

Numerical results confirm improved accuracy

Abstract

The random batch method is advantageous in accelerating force calculations in particle simulations, but it poses a challenge of removing the artificial heating effect in application to the Langevin dynamics. We develop an approach to solve this issue by estimating the force variance, resulting in a variance-reduced random batch Langevin dynamics. Theoretical analysis shows the high-order local truncation error of the time step in the numerical discretization scheme, in consistent with the fluctuation-dissipation theorem. Numerical results indicate that the method can achieve a significant variance reduction since a smaller batch size provides accurate approximation, demonstrating the attractive feature of the variance-reduced random batch method for Langevin dynamics.