Slow-scale split-step tau-leap method for stiff stochastic chemical systems

TL;DR

This paper introduces a slow-scale split-step tau-leap method designed to efficiently simulate stiff stochastic chemical systems, accurately capturing mean and variance even in highly stiff scenarios.

Contribution

It proposes a novel splitting heuristic with parameter estimation from moment equations, improving numerical stability and accuracy for stiff stochastic systems.

Findings

Reproduces exact mean and variance for linear test equations

Demonstrates good accuracy in arbitrarily stiff linear systems

Shows efficiency in numerical examples for linear and nonlinear systems

Abstract

Tau-leaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. Motivation for the development of such methods can be found, for instance, in the fields of chemical kinetics and systems biology. It is known that the dynamical behavior of biochemical systems is often intrinsically stiff representing a serious challenge for their numerical approximation. The naive extension of stiff deterministic solvers to stochastic integration often yields numerical solutions with either impractically large relaxation times or incorrectly resolved covariance. In this paper, we propose a splitting heuristic which helps to resolve some of these issues. The proposed integrator contains a number of unknown parameters which are estimated for each particular problem from the moment equations of the corresponding linearized system. We show that this method is able to reproduce the exact mean and variance of the linear scalar test equation and demonstrates a good accuracy for the arbitrarily stiff systems at least in the linear case. The numerical examples for both linear and nonlinear systems are also provided and the obtained results confirm the efficiency of the considered splitting approach.