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# 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:
- 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:
- 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 Field | Value | Language |
---|---|---|

dc.contributor.author | Moraes, Alvaro | en |

dc.date.accessioned | 2017-06-05T08:35:49Z | - |

dc.date.available | 2017-06-05T08:35:49Z | - |

dc.date.issued | 2015-01-07 | - |

dc.identifier.uri | http://hdl.handle.net/10754/624109 | - |

dc.description.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. | en |

dc.relation.url | http://mediasite.kaust.edu.sa/Mediasite/Play/869e9e5ed1424f18ac2ca76f04709c421d?catalog=ca65101c-a4eb-4057-9444-45f799bd9c52 | en |

dc.title | Hybrid Multilevel Monte Carlo Simulation of Stochastic Reaction Networks | en |

dc.type | Presentation | en |

dc.contributor.department | Computer, Electrical and Mathematical Sciences & Engineering (CEMSE) | en |

dc.conference.date | January 6-9, 2015 | en |

dc.conference.name | Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015) | en |

dc.conference.location | KAUST | en |

kaust.author | Moraes, Alvaro | en |

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