Approximate Exponential Algorithms to Solve the Chemical Master Equation

TL;DR

This paper introduces new approximate exponential algorithms for solving the chemical master equation, leveraging matrix exponential approximations to improve stochastic chemical kinetics simulations.

Contribution

It presents novel algorithms that exploit linearity and matrix exponential approximations, offering potentially faster stochastic simulation methods for chemical kinetics.

Findings

New algorithms outperform traditional methods in certain scenarios

Numerical experiments demonstrate improved efficiency

Approximations maintain accuracy while accelerating simulations

Abstract

This paper discusses new simulation algorithms for stochastic chemical kinetics that exploit the linearity of the chemical master equation and its matrix exponential exact solution. These algorithms make use of various approximations of the matrix exponential to evolve probability densities in time. A sampling of the approximate solutions of the chemical master equation is used to derive accelerated stochastic simulation algorithms. Numerical experiments compare the new methods with the established stochastic simulation algorithm and the tau-leaping method.