Metadynamics for transition paths in irreversible dynamics

TL;DR

This paper introduces a method using pathspace metadynamics to efficiently sample and analyze transition paths in metastable stochastic systems, including irreversible and time-dependent cases, providing insights into multiple transition mechanisms.

Contribution

It extends pathspace metadynamics from reversible to irreversible and time-dependent stochastic systems, enabling rigorous estimation of transition path probabilities.

Findings

Pathspace metadynamics can sample transition paths in irreversible systems.

The method accurately estimates probabilities of different transition channels.

Application to magnetic field reversal PDE demonstrates practical utility.

Abstract

Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic systems, these transitions can happen via multiple physical mechanisms, corresponding to multiple distinct transition channels for a pair of states. In this paper, we use the fact that the transition path ensemble is equivalent to the invariant measure of a gradient flow in pathspace, which can be efficiently sampled via metadynamics. We demonstrate how this pathspace metadynamics, previously restricted to reversible molecular dynamics, is in fact very generally applicable to metastable stochastic systems, including irreversible and time-dependent ones, and allows to estimate rigorously the relative probability of competing transition paths. We showcase this approach on the study of a stochastic partial differential equation describing magnetic field reversal in the presence of advection.