Approximate Exponential Algorithms to Solve the Chemical Master Equation
This work addresses the computational bottleneck of simulating stochastic chemical kinetics for systems with many species and reactions, offering faster approximate methods.
The authors develop new simulation algorithms for stochastic chemical kinetics by approximating the matrix exponential solution of the chemical master equation, achieving accelerated stochastic simulation. Numerical experiments show the new methods outperform the standard stochastic simulation algorithm and tau-leaping in efficiency.
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.