Hybrid Multilevel Monte Carlo Simulation of Stochastic Reaction Networks

Handle URI:
http://hdl.handle.net/10754/624109
Title:
Hybrid Multilevel Monte Carlo Simulation of Stochastic Reaction Networks
Authors:
Moraes, Alvaro ( 0000-0003-4144-1243 )
Abstract:
Stochastic reaction networks (SRNs) is a class of continuous-time Markov chains intended to describe, from the kinetic point of view, the time-evolution of chemical systems in which molecules of different chemical species undergo a finite set of reaction channels. This talk is based on articles [4, 5, 6], where we are interested in the following problem: given a SRN, X, defined though its set of reaction channels, and its initial state, x0, estimate E (g(X(T))); that is, the expected value of a scalar observable, g, of the process, X, at a fixed time, T. This problem lead us to define a series of Monte Carlo estimators, M, such that, with high probability can produce values close to the quantity of interest, E (g(X(T))). More specifically, given a user-selected tolerance, TOL, and a small confidence level, η, find an estimator, M, based on approximate sampled paths of X, such that, P (|E (g(X(T))) − M| ≤ TOL) ≥ 1 − η; even more, we want to achieve this objective with near optimal computational work. We first introduce a hybrid path-simulation scheme based on the well-known stochastic simulation algorithm (SSA)[3] and the tau-leap method [2]. Then, we introduce a Multilevel Monte Carlo strategy that allows us to achieve a computational complexity of order O(T OL−2), this is the same computational complexity as in an exact method but with a smaller constant. We provide numerical examples to show our results.
KAUST Department:
Computer, Electrical and Mathematical Sciences & Engineering (CEMSE)
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
Issue Date:
7-Jan-2015
Type:
Presentation
Additional Links:
http://mediasite.kaust.edu.sa/Mediasite/Play/869e9e5ed1424f18ac2ca76f04709c421d?catalog=ca65101c-a4eb-4057-9444-45f799bd9c52
Appears in Collections:
Presentations; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

Full metadata record

DC FieldValue Language
dc.contributor.authorMoraes, Alvaroen
dc.date.accessioned2017-06-05T08:35:49Z-
dc.date.available2017-06-05T08:35:49Z-
dc.date.issued2015-01-07-
dc.identifier.urihttp://hdl.handle.net/10754/624109-
dc.description.abstractStochastic reaction networks (SRNs) is a class of continuous-time Markov chains intended to describe, from the kinetic point of view, the time-evolution of chemical systems in which molecules of different chemical species undergo a finite set of reaction channels. This talk is based on articles [4, 5, 6], where we are interested in the following problem: given a SRN, X, defined though its set of reaction channels, and its initial state, x0, estimate E (g(X(T))); that is, the expected value of a scalar observable, g, of the process, X, at a fixed time, T. This problem lead us to define a series of Monte Carlo estimators, M, such that, with high probability can produce values close to the quantity of interest, E (g(X(T))). More specifically, given a user-selected tolerance, TOL, and a small confidence level, η, find an estimator, M, based on approximate sampled paths of X, such that, P (|E (g(X(T))) − M| ≤ TOL) ≥ 1 − η; even more, we want to achieve this objective with near optimal computational work. We first introduce a hybrid path-simulation scheme based on the well-known stochastic simulation algorithm (SSA)[3] and the tau-leap method [2]. Then, we introduce a Multilevel Monte Carlo strategy that allows us to achieve a computational complexity of order O(T OL−2), this is the same computational complexity as in an exact method but with a smaller constant. We provide numerical examples to show our results.en
dc.relation.urlhttp://mediasite.kaust.edu.sa/Mediasite/Play/869e9e5ed1424f18ac2ca76f04709c421d?catalog=ca65101c-a4eb-4057-9444-45f799bd9c52en
dc.titleHybrid Multilevel Monte Carlo Simulation of Stochastic Reaction Networksen
dc.typePresentationen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE)en
dc.conference.dateJanuary 6-9, 2015en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)en
dc.conference.locationKAUSTen
kaust.authorMoraes, Alvaroen
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