Statistical Mechanics of Histories: A Cluster Monte Carlo Algorithm

TL;DR

This paper introduces a novel cluster Monte Carlo algorithm for efficiently sampling histories of nonlinear stochastic processes, improving simulation of rare events and parameter estimation in complex systems.

Contribution

The paper presents a new cluster algorithm that enhances sampling efficiency for histories in stochastic systems using a path integral framework.

Findings

Improved sampling efficiency by up to an order of magnitude in $\

Effective for simulating rare events and estimating states and parameters.

Applicable to $\

Abstract

We present an efficient computational approach to sample the histories of nonlinear stochastic processes. This framework builds upon recent work on casting a $d$-dimensional stochastic dynamical system into a $d+1$-dimensional equilibrium system using the path integral approach. We introduce a cluster algorithm that efficiently samples histories and discuss how to include measurements that are available into the estimate of the histories. This allows our approach to be applicable to the simulation of rare events and to optimal state and parameter estimation. We demonstrate the utility of this approach for $\phi^4$ Langevin dynamics in two spatial dimensions where our algorithm improves sampling efficiency up to an order of magnitude.