Sampling diffusive transition paths

TL;DR

This paper introduces a new symmetric sampling method for diffusive transition paths that efficiently handles stiffness issues and enables parallel computation, demonstrated on Lennard-Jones cluster transitions.

Contribution

It presents a symmetric Onsager-Machlup-based path sampling approach combined with the FSA and S&S algorithms for efficient, parallel sampling of long diffusive paths.

Findings

The method accurately samples transition paths for complex systems.

The S&S algorithm enables parallel computation of long trajectories.

Application to Lennard-Jones cluster shows effective sampling of structural transitions.

Abstract

We address the problem of sampling double-ended diffusive paths. The ensemble of paths is expressed using a symmetric version of the Onsager-Machlup formula, which only requires evaluation of the force field and which, upon direct time discretization, gives rise to a symmetric integrator that is accurate to second order. Efficiently sampling this ensemble requires avoiding the well-known stiffness problem associated with sampling infinitesimal Brownian increments of the path, as well as a different type of stiffness associated with sampling the coarse features of long paths. The fine-feature sampling stiffness is eliminated with the use of the fast sampling algorithm (FSA), and the coarse-feature sampling stiffness is avoided by introducing the sliding and sampling (S&S) algorithm. A key feature of the S&S algorithm is that it enables massively parallel computers to sample diffusive trajectories that are long in time. We use the algorithm to sample the transition path ensemble for the structural interconversion of the 38-atom Lennard-Jones cluster at low temperature.