Random Batch Methods for classical and quantum interacting particle systems and statistical samplings

TL;DR

This paper reviews Random Batch Methods (RBM) that efficiently simulate large classical and quantum interacting particle systems by reducing computational costs from quadratic to linear, applicable across various scientific fields.

Contribution

It provides a comprehensive overview of RBM techniques for classical and quantum systems, including theory, applications, and potential for large-scale simulations.

Findings

RBM reduces computational complexity from O(N^2) to O(N).

Applicable to molecular dynamics, statistical sampling, and quantum Monte Carlo.

Demonstrates effectiveness in classical and quantum particle simulations.

Abstract

We review the Random Batch Methods (RBM) for interacting particle systems consisting of $N$-particles, with $N$ being large. The computational cost of such systems is of $O(N^2)$, which is prohibitively expensive. The RBM methods use small but random batches so the computational cost is reduced, per time step, to $O(N)$. In this article we discuss these methods for both classical and quantum systems, the corresponding theory, and applications from molecular dynamics, statistical samplings, to agent-based models for collective behavior, and quantum Monte-Carlo methods.