Weighted-ensemble Brownian dynamics simulation: Sampling of rare events in non-equilibrium systems

TL;DR

This paper introduces a weighted-ensemble algorithm for efficiently sampling steady states and rare events in non-equilibrium stochastic systems, achieving unprecedented accuracy in probability and rate calculations.

Contribution

The authors develop a novel weighted-ensemble method capable of sampling non-potential systems without detailed balance, accurately estimating extremely rare probabilities and rates.

Findings

Successfully computed steady state probabilities as low as 10^{-300}

Reproduced Arrhenius law for rates around 10^{-280}

Demonstrated improved efficiency over standard Brownian dynamics and existing WE methods

Abstract

We provide an algorithm based on weighted-ensemble (WE) methods, to accurately sample systems at steady state. Applying our method to different one- and two-dimensional models, we succeed to calculate steady state probabilities of order $10^{-300}$ and reproduce Arrhenius law for rates of order $10^{-280}$. Special attention is payed to the simulation of non-potential systems where no detailed balance assumption exists. For this large class of stochastic systems, the stationary probability distribution density is often unknown and cannot be used as preknowledge during the simulation. We compare the algorithms efficiency with standard Brownian dynamics simulations and other WE methods.