A multilevel adaptive reaction-splitting simulation method for stochastic reaction networks

In this work, we present a novel multilevel Monte Carlo method for kinetic simulation of stochastic reaction networks characterized by having simultaneously fast and slow reaction channels. To produce efficient simulations, our method adaptively classifies the reactions channels into fast and slow channels. To this end, we first introduce a state-dependent quantity named level of activity of a reaction channel. Then, we propose a low-cost heuristic that allows us to adaptively split the set of reaction channels into two subsets characterized by either a high or a low level of activity. Based on a time-splitting technique, the increments associated with high-activity channels are simulated using the tau-leap method, while those associated with low-activity channels are simulated using an exact method. This path simulation technique is amenable for coupled path generation and a corresponding multilevel Monte Carlo algorithm. To estimate expected values of observables of the system at a prescribed final time, our method bounds the global computational error to be below a prescribed tolerance, TOL, within a given confidence level. This goal is achieved with a computational complexity of order O(TOL^-2), the same as with a pathwise-exact method, but with a smaller constant. We also present a novel low-cost control variate technique based on the stochastic time change representation by Kurtz, showing its performance on a numerical example. We present two numerical examples extracted from the literature that show how the reaction-splitting method obtains substantial gains with respect to the standard stochastic simulation algorithm and the multilevel Monte Carlo approach by Anderson and Higham.