Forward Flux Sampling-type schemes for simulating rare events: Efficiency analysis

TL;DR

This paper analyzes the efficiency of Forward Flux Sampling-type schemes for simulating rare events in stochastic systems, providing analytical tools to compare methods, optimize parameters, and predict computational costs and errors.

Contribution

It derives analytical expressions for cost and error in rare event simulation methods, enabling better method selection and parameter optimization.

Findings

Analytical expressions accurately predict computational efficiency.

Application to a non-equilibrium problem validates the predictions.

Guidelines for choosing optimal simulation parameters.

Abstract

We analyse the efficiency of several simulation methods which we have recently proposed for calculating rate constants for rare events in stochastic dynamical systems, in or out of equilibrium. We derive analytical expressions for the computational cost of using these methods, and for the statistical error in the final estimate of the rate constant, for a given computational cost. These expressions can be used to determine which method to use for a given problem, to optimize the choice of parameters, and to evaluate the significance of the results obtained. We apply the expressions to the two-dimensional non-equilibrium rare event problem proposed by Maier and Stein. For this problem, our analysis gives accurate quantitative predictions for the computational efficiency of the three methods.