Path sampling with Stochastic Dynamics: Some new Algorithms

TL;DR

This paper introduces new algorithms for Path Sampling with stochastic dynamics, including a novel proposal function and a switching strategy, improving sampling efficiency and enabling constrained path sampling and simulated annealing.

Contribution

The paper presents a new 'brownian tube' proposal function and a finite-rate switching strategy for path sampling with stochastic dynamics, enhancing efficiency and flexibility.

Findings

The 'brownian tube' proposal improves decorrelation in path space.

Switching strategy enables equilibrium transformations at finite rates.

Methods facilitate constrained path sampling and simulated annealing.

Abstract

We propose here some new sampling algorithms for Path Sampling in the case when stochastic dynamics are used. In particular, we present a new proposal function for equilibrium sampling of paths with a Monte-Carlo dynamics (the so-called ``brownian tube'' proposal). This proposal is based on the continuity of the dynamics with respect to the random forcing, and generalizes all previous approaches. The efficiency of this proposal is demonstrated using some measure of decorrelation in path space. We also discuss a switching strategy that allows to transform ensemble of paths at a finite rate while remaining at equilibrium, in contrast with the usual Jarzynski like switching. This switching is very interesting to sample constrained paths starting from unconstrained paths, or to perform simulated annealing in a rigorous way.