Simulating rare events in equilibrium or nonequilibrium stochastic systems

TLDR

The authors present three algorithms for calculating rate constants and sampling transition paths for rare events in stochastic dynamics simulations. The algorithms employ a series of interfaces in phase space to generate transition paths as chains of partial paths without assuming a path distribution, are applicable to equilibrium or non‑equilibrium stationary systems, and were tested on kinetic Monte Carlo genetic switch and Langevin polymer translocation simulations. All three methods exhibit comparable efficiency and are far more efficient than brute‑force simulation.

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.