Non-Stationary Forward Flux Sampling

TL;DR

This paper introduces Non-Stationary Forward Flux Sampling, a novel simulation method for efficiently estimating rare event probabilities in both stationary and non-stationary stochastic systems, including complex non-Markovian and driven systems.

Contribution

It develops a new sampling technique that handles time-dependent and non-stationary dynamics, extending the applicability of rare event simulations beyond traditional stationary frameworks.

Findings

Accurately estimates time-dependent switching propensities.

Validates method with exact solution for a barrier crossing problem.

Demonstrates usefulness in modeling genetic toggle switch dynamics.

Abstract

We present a new method, Non-Stationary Forward Flux Sampling, that allows efficient simulation of rare events in both stationary and non-stationary stochastic systems. The method uses stochastic branching and pruning to achieve uniform sampling of trajectories in phase space and time, leading to accurate estimates for time-dependent switching propensities and time-dependent phase space probability densities. The method is suitable for equilibrium or non-equilibrium systems, in or out of stationary state, including non-Markovian or externally driven systems. We demonstrate the validity of the technique by applying it to a one-dimensional barrier crossing problem that can be solved exactly, and show its usefulness by applying it to the time-dependent switching of a genetic toggle switch.