Onsager-Machlup action-based path sampling and its combination with replica exchange for diffusive and multiple pathways

TL;DR

This paper introduces a novel path sampling method based on the Onsager-Machlup action functional, transforming paths into Fourier space and combining with replica exchange to efficiently sample multiple pathways in complex energy landscapes.

Contribution

The paper presents a new action-based path sampling technique using Fourier transforms and integrates replica exchange to improve sampling of multiple pathways in rugged landscapes.

Findings

Successfully demonstrated on a 2D bifurcated potential system

Compared favorably with conventional transition path sampling

Discussed discretization errors and their impact

Abstract

For sampling multiple pathways in a rugged energy landscape, we propose a novel action-based path sampling method using the Onsager-Machlup action functional. Inspired by the Fourier-path integral simulation of a quantum mechanical system, a path in Cartesian space is transformed into that in Fourier space, and an overdamped Langevin equation is derived for the Fourier components to achieve a canonical ensemble of the path at a finite temperature. To avoid "path trapping" around an initially guessed path, the path sampling method is further combined with a powerful sampling technique, the replica exchange method. The principle and algorithm of our method is numerically demonstrated for a model two-dimensional system with a bifurcated potential landscape. The results are compared with those of conventional transition path sampling and the equilibrium theory, and the error due to path discretization is also discussed.