Handle URI:
http://hdl.handle.net/10754/624110
Title:
Multi-Index Monte Carlo (MIMC) When sparsity meets sampling
Authors:
Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
This talk focuses into our newest method: Multi Index Monte Carlo (MIMC). The MIMC method uses a stochastic combination technique to solve the given approximation problem, generalizing the notion of standard MLMC levels into a set of multi indices that should be properly chosen to exploit the available regularity. Indeed, instead of using first-order differences as in standard MLMC, MIMC uses high-order differences to reduce the variance of the hierarchical differences dramatically. This in turn gives a new improved complexity result that increases the domain of the problem parameters for which the method achieves the optimal convergence rate, O(TOL-2). Using optimal index sets that we determined, MIMC achieves a better rate for the computational complexity does not depend on the dimensionality of the underlying problem, up to logarithmic factors. We present numerical results related to a three dimensional PDE with random coefficients to substantiate some of the derived computational complexity rates. Finally, using the Lindeberg-Feller theorem, we also show the asymptotic normality of the statistical error in the MIMC estimator and justify in this way our error estimate that allows prescribing both the required accuracy and confidence in the final result
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/8cab8cbeec4245ce86802bcc342a187c1d?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.authorTempone, Raulen
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/10754/624110-
dc.description.abstractThis talk focuses into our newest method: Multi Index Monte Carlo (MIMC). The MIMC method uses a stochastic combination technique to solve the given approximation problem, generalizing the notion of standard MLMC levels into a set of multi indices that should be properly chosen to exploit the available regularity. Indeed, instead of using first-order differences as in standard MLMC, MIMC uses high-order differences to reduce the variance of the hierarchical differences dramatically. This in turn gives a new improved complexity result that increases the domain of the problem parameters for which the method achieves the optimal convergence rate, O(TOL-2). Using optimal index sets that we determined, MIMC achieves a better rate for the computational complexity does not depend on the dimensionality of the underlying problem, up to logarithmic factors. We present numerical results related to a three dimensional PDE with random coefficients to substantiate some of the derived computational complexity rates. Finally, using the Lindeberg-Feller theorem, we also show the asymptotic normality of the statistical error in the MIMC estimator and justify in this way our error estimate that allows prescribing both the required accuracy and confidence in the final resulten
dc.relation.urlhttp://mediasite.kaust.edu.sa/Mediasite/Play/8cab8cbeec4245ce86802bcc342a187c1d?catalog=ca65101c-a4eb-4057-9444-45f799bd9c52en
dc.titleMulti-Index Monte Carlo (MIMC) When sparsity meets samplingen
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.authorTempone, Raulen
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