Multilevel hybrid split-step implicit tau-leap

Handle URI:
http://hdl.handle.net/10754/621403
Title:
Multilevel hybrid split-step implicit tau-leap
Authors:
Ben Hammouda, Chiheb ( 0000-0002-8386-0406 ) ; Moraes, Alvaro ( 0000-0003-4144-1243 ) ; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
In biochemically reactive systems with small copy numbers of one or more reactant molecules, the dynamics is dominated by stochastic effects. To approximate those systems, discrete state-space and stochastic simulation approaches have been shown to be more relevant than continuous state-space and deterministic ones. In systems characterized by having simultaneously fast and slow timescales, existing discrete space-state stochastic path simulation methods, such as the stochastic simulation algorithm (SSA) and the explicit tau-leap (explicit-TL) method, can be very slow. Implicit approximations have been developed to improve numerical stability and provide efficient simulation algorithms for those systems. Here, we propose an efficient Multilevel Monte Carlo (MLMC) method in the spirit of the work by Anderson and Higham (SIAM Multiscal Model. Simul. 10(1), 2012). This method uses split-step implicit tau-leap (SSI-TL) at levels where the explicit-TL method is not applicable due to numerical stability issues. We present numerical examples that illustrate the performance of the proposed method. © 2016 Springer Science+Business Media New York
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Citation:
Ben Hammouda C, Moraes A, Tempone R (2016) Multilevel hybrid split-step implicit tau-leap. Numerical Algorithms. Available: http://dx.doi.org/10.1007/s11075-016-0158-z.
Publisher:
Springer Nature
Journal:
Numerical Algorithms
Issue Date:
17-Jun-2016
DOI:
10.1007/s11075-016-0158-z
Type:
Article
ISSN:
1017-1398; 1572-9265
Sponsors:
Clean Combustion Center at King Abdullah University of Science and Technology
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBen Hammouda, Chiheben
dc.contributor.authorMoraes, Alvaroen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2016-11-03T08:28:28Z-
dc.date.available2016-11-03T08:28:28Z-
dc.date.issued2016-06-17en
dc.identifier.citationBen Hammouda C, Moraes A, Tempone R (2016) Multilevel hybrid split-step implicit tau-leap. Numerical Algorithms. Available: http://dx.doi.org/10.1007/s11075-016-0158-z.en
dc.identifier.issn1017-1398en
dc.identifier.issn1572-9265en
dc.identifier.doi10.1007/s11075-016-0158-zen
dc.identifier.urihttp://hdl.handle.net/10754/621403-
dc.description.abstractIn biochemically reactive systems with small copy numbers of one or more reactant molecules, the dynamics is dominated by stochastic effects. To approximate those systems, discrete state-space and stochastic simulation approaches have been shown to be more relevant than continuous state-space and deterministic ones. In systems characterized by having simultaneously fast and slow timescales, existing discrete space-state stochastic path simulation methods, such as the stochastic simulation algorithm (SSA) and the explicit tau-leap (explicit-TL) method, can be very slow. Implicit approximations have been developed to improve numerical stability and provide efficient simulation algorithms for those systems. Here, we propose an efficient Multilevel Monte Carlo (MLMC) method in the spirit of the work by Anderson and Higham (SIAM Multiscal Model. Simul. 10(1), 2012). This method uses split-step implicit tau-leap (SSI-TL) at levels where the explicit-TL method is not applicable due to numerical stability issues. We present numerical examples that illustrate the performance of the proposed method. © 2016 Springer Science+Business Media New Yorken
dc.description.sponsorshipClean Combustion Center at King Abdullah University of Science and Technologyen
dc.publisherSpringer Natureen
dc.subjectMultilevel Monte Carloen
dc.titleMultilevel hybrid split-step implicit tau-leapen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalNumerical Algorithmsen
kaust.authorBen Hammouda, Chiheben
kaust.authorMoraes, Alvaroen
kaust.authorTempone, Raulen
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