A Multilevel Adaptive Reaction-splitting Simulation Method for Stochastic Reaction Networks

Handle URI:
http://hdl.handle.net/10754/621915
Title:
A Multilevel Adaptive Reaction-splitting Simulation Method for Stochastic Reaction Networks
Authors:
Moraes, Alvaro ( 0000-0003-4144-1243 ) ; Tempone, Raul ( 0000-0003-1967-4446 ) ; Vilanova, Pedro ( 0000-0001-6620-6261 )
Abstract:
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
Issue Date:
7-Jul-2016
DOI:
10.1137/140972081
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This work was supported by King Abdullah University of Science and Technology (KAUST)
Additional Links:
http://epubs.siam.org/doi/10.1137/140972081
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorMoraes, Alvaroen
dc.contributor.authorTempone, Raulen
dc.contributor.authorVilanova, Pedroen
dc.date.accessioned2016-12-01T14:12:42Z-
dc.date.available2016-12-01T14:12:42Z-
dc.date.issued2016-07-07en
dc.identifier.citationMoraes 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.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/140972081en
dc.identifier.urihttp://hdl.handle.net/10754/621915-
dc.description.abstractIn 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.en
dc.description.sponsorshipThis work was supported by King Abdullah University of Science and Technology (KAUST)en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/140972081en
dc.rightsArchived with thanks to SIAM Journal on Scientific Computingen
dc.subjectAdaptive reaction splittingen
dc.subjectChernoff tau-leapen
dc.subjectControl variatesen
dc.subjectError controlen
dc.subjectError estimatesen
dc.subjectHybrid algorithmsen
dc.subjectMultilevel Monte Carloen
dc.subjectWeak approximationen
dc.titleA Multilevel Adaptive Reaction-splitting Simulation Method for Stochastic Reaction Networksen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.eprint.versionPublisher's Version/PDFen
kaust.authorMoraes, Alvaroen
kaust.authorTempone, Raulen
kaust.authorVilanova, Pedroen
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