Simulating rare events in equilibrium or non-equilibrium stochastic systems

TL;DR

This paper introduces three novel algorithms for efficiently sampling rare transition events in stochastic systems, applicable to both equilibrium and non-equilibrium stationary states, without prior phase space knowledge.

Contribution

The paper presents three new algorithms that generate transition paths using interfaces in phase space, improving efficiency over brute force methods for rare event sampling.

Findings

All three methods have comparable efficiency.

Methods outperform brute force simulation significantly.

Applicable to kinetic Monte Carlo and Langevin Dynamics simulations.

Abstract

We present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics. The methods do not require a priori knowledge of the phase space density and are suitable for equilibrium or non-equilibrium systems in stationary state. All the methods use a series of interfaces in phase space, between the initial and final states, to generate transition paths as chains of connected partial paths, in a ratchet-like manner. No assumptions are made about the distribution of paths at the interfaces. The three methods differ in the way that the transition path ensemble is generated. We apply the algorithms to kinetic Monte Carlo simulations of a genetic switch and to Langevin Dynamics simulations of intermittently driven polymer translocation through a pore. We find that the three methods are all of comparable efficiency, and that all the methods are much more efficient than brute force simulation.