Time-parallel simulation of stochastic chemical kinetics

Abstract

A version of the time-parallel algorithm parareal is suggested for the simulation of stochastic models in chemical kinetics. A fast solver at the coarse scale is available in the form of the usual macroscopic rate equations. A stochastic simulation is used to obtain an exact realization of the process at the mesoscopic scale. With the parareal algorithm, this expensive simulation can be performed in parallel. The underlying stochastic description is a jump process driven by the Poisson random measure. Convergence results suggests that a homogenization of the solution is advantageous and a simple but highly general such technique is devised. A numerical experiment on a model representative to the field of computational systems biology serves as an illustration. The conclusion is that the method builds an attractive bridge between on the one hand, macroscopic deterministic scales and, on the other hand, mesoscopic stochastic ones. This construction is clearly possible to apply to stochastic problems within other fields. © 2008 American Institute of Physics.