Towards Automatic Global Error Control: Computable Weak Error Expansion for the Tau-Leap Method

TL;DR

This paper introduces new error expansion techniques with computable leading terms for the global weak error in tau-leap methods, enabling adaptive algorithms for stochastic jump processes in kinetic Monte Carlo models.

Contribution

It develops novel a posteriori and a priori error estimates with computable leading order terms for the tau-leap method, enhancing error control in stochastic simulations.

Findings

Derived computable weak error expansions for tau-leap

Provided adaptive algorithms based on error estimates

Compared tau-leap and exact simulation efficiencies

Abstract

This work develops novel error expansions with computable leading order terms for the global weak error in the tau-leap discretization of pure jump processes arising in kinetic Monte Carlo models. Accurate computable a posteriori error approximations are the basis for adaptive algorithms; a fundamental tool for numerical simulation of both deterministic and stochastic dynamical systems. These pure jump processes are simulated either by the tau-leap method, or by exact simulation, also referred to as dynamic Monte Carlo, the Gillespie algorithm or the Stochastic simulation algorithm. Two types of estimates are presented: an a priori estimate for the relative error that gives a comparison between the work for the two methods depending on the propensity regime, and an a posteriori estimate with computable leading order term.