On the Random Batch Method for second order interacting particle systems

TL;DR

This paper analyzes the Random Batch Method (RBM) for second order interacting particle systems, proving convergence and extending its application to singular kernels in molecular dynamics.

Contribution

It establishes uniform-in-time convergence for RBM in second order systems and introduces a kernel splitting strategy for singular interactions.

Findings

Proved uniform-in-time strong convergence of RBM

Developed kernel splitting strategy for singular kernels

Numerical investigation in molecular dynamics

Abstract

We investigate several important issues regarding the Random Batch Method (RBM) for second order interacting particle systems. We first show the uniform-in-time strong convergence for second order systems under suitable contraction conditions. Secondly, we propose the application of RBM for singular interaction kernels via kernel splitting strategy, and investigate numerically the application to molecular dynamics.