Importance sampling of unbounded random stopping times: computing committor functions and exit rates without reweighting

TL;DR

This paper develops importance sampling methods for rare event simulation in molecular dynamics, enabling the computation of committor functions and exit rates without reweighting long trajectories, thus improving efficiency and accuracy.

Contribution

It introduces a variational importance sampling framework that reduces variance and avoids reweighting for unbounded stopping times in rare event simulations.

Findings

Variance reduction in rare event estimators

Methods applicable to long, unbounded trajectories

Numerical validation on benchmark examples

Abstract

Rare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare transitions is that they happen on timescales that are on average exponentially long compared to the characteristic timescale of the system, with waiting time distributions that have (sub)exponential tails and infinite support. As a result, sampling such rare events can lead to trajectories that can be become arbitrarily long, with not too low probability, which makes the reweighting of such trajectories a real challenge. Here, we discuss rare event simulation by importance sampling from a variational perspective, with a focus on applications in molecular dynamics, in particular the computation of committor functions. The idea is to design importance sampling schemes that (a) reduce the variance of a rare event estimator while controlling the average length of the trajectories and (b) that do not require the reweighting of possibly very long trajectories. In doing so, we study different stochastic control formulations for committor and mean first exit times, which we compare both from a theoretical and a computational point of view, including numerical studies of some benchmark examples.