A Multilevel Adaptive Reaction-splitting Simulation Method for Stochastic Reaction Networks
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2016-07-07Online Publication Date
2016-07-07Print Publication Date
2016-01Permanent link to this record
http://hdl.handle.net/10754/621915
Metadata
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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. © 2016 Society for Industrial and Applied Mathematics.Citation
Moraes A, Tempone R, Vilanova P (2016) A Multilevel Adaptive Reaction-splitting Simulation Method for Stochastic Reaction Networks. SIAM Journal on Scientific Computing 38: A2091–A2117. Available: http://dx.doi.org/10.1137/140972081.Sponsors
This work was supported by King Abdullah University of Science and Technology (KAUST)arXiv
1406.1989Additional Links
http://epubs.siam.org/doi/10.1137/140972081ae974a485f413a2113503eed53cd6c53
10.1137/140972081