Improved diffusion Monte Carlo

TL;DR

This paper introduces an improved diffusion Monte Carlo algorithm that reduces variance and enhances efficiency, making it practical for complex rare event simulations and high-frequency data assimilation tasks.

Contribution

It combines RESTART and DPR algorithms with DMC to significantly lower variance, enabling applications previously hindered by exponential variance growth.

Findings

Lower variance per workload across regimes

Feasible application to rare event and data assimilation problems

Demonstrated effectiveness on Lennard-Jones cluster and high-frequency data

Abstract

We propose a modification, based on the RESTART (repetitive simulation trials after reaching thresholds) and DPR (dynamics probability redistribution) rare event simulation algorithms, of the standard diffusion Monte Carlo (DMC) algorithm. The new algorithm has a lower variance per workload, regardless of the regime considered. In particular, it makes it feasible to use DMC in situations where the "na\"ive" generalisation of the standard algorithm would be impractical, due to an exponential explosion of its variance. We numerically demonstrate the effectiveness of the new algorithm on a standard rare event simulation problem (probability of an unlikely transition in a Lennard-Jones cluster), as well as a high-frequency data assimilation problem.