Performance evaluation of generalized polynomial chaos

Dongbin Xiu; Didier Lucor; C. H. Su; George Em Karniadakis

doi:10.1007/3-540-44864-0_36

Performance evaluation of generalized polynomial chaos

Dongbin Xiu
, Didier Lucor
, C. H. Su
, George Em Karniadakis

Women and Infants Hospital of Rhode Island-Warren Alpert Medical School of Brown University

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Chapitre › Revue par des pairs

Résumé

In this paper we review some applications of generalized polynomial chaos expansion for uncertainty quantification. The mathematical framework is presented and the convergence of the method is demonstrated for model problems. In particular, we solve the first-order and second-order ordinary differential equations with random parameters, and examine the efficiency of generalized polynomial chaos compared to Monte Carlo simulations. It is shown that the generalized polynomial chaos can be orders of magnitude more efficient than Monte Carlo simulations when the dimensionality of random input is low, e.g. for correlated noise.

langue originale	Anglais
titre	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
rédacteurs en chef	Peter M. A. Sloot, David Abramson, Alexander V. Bogdanov, Yuriy E. Gorbachev, Jack J. Dongarra, Albert Y. Zomaya
Editeur	Springer Verlag
Pages	346-354
Nombre de pages	9
ISBN (imprimé)	3540401970, 9783540401971
Les DOIs	https://doi.org/10.1007/3-540-44864-0_36
état	Publié - 1 janv. 2003
Modification externe	Oui

Série de publications

Nom	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2660
ISSN (imprimé)	0302-9743
ISSN (Electronique)	1611-3349

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10.1007/3-540-44864-0_36

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Xiu, D., Lucor, D., Su, C. H., & Karniadakis, G. E. (2003). Performance evaluation of generalized polynomial chaos. Dans P. M. A. Sloot, D. Abramson, A. V. Bogdanov, Y. E. Gorbachev, J. J. Dongarra, & A. Y. Zomaya (eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (p. 346-354). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol 2660). Springer Verlag. https://doi.org/10.1007/3-540-44864-0_36

Xiu, Dongbin ; Lucor, Didier ; Su, C. H. et al. / Performance evaluation of generalized polynomial chaos. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Editeur / Peter M. A. Sloot ; David Abramson ; Alexander V. Bogdanov ; Yuriy E. Gorbachev ; Jack J. Dongarra ; Albert Y. Zomaya. Springer Verlag, 2003. p. 346-354 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Performance evaluation of generalized polynomial chaos",

abstract = "In this paper we review some applications of generalized polynomial chaos expansion for uncertainty quantification. The mathematical framework is presented and the convergence of the method is demonstrated for model problems. In particular, we solve the first-order and second-order ordinary differential equations with random parameters, and examine the efficiency of generalized polynomial chaos compared to Monte Carlo simulations. It is shown that the generalized polynomial chaos can be orders of magnitude more efficient than Monte Carlo simulations when the dimensionality of random input is low, e.g. for correlated noise.",

author = "Dongbin Xiu and Didier Lucor and Su, \{C. H.\} and Karniadakis, \{George Em\}",

year = "2003",

month = jan,

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doi = "10.1007/3-540-44864-0\_36",

language = "English",

isbn = "3540401970",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "346--354",

editor = "Sloot, \{Peter M. A.\} and David Abramson and Bogdanov, \{Alexander V.\} and Gorbachev, \{Yuriy E.\} and Dongarra, \{Jack J.\} and Zomaya, \{Albert Y.\}",

booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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Xiu, D, Lucor, D, Su, CH & Karniadakis, GE 2003, Performance evaluation of generalized polynomial chaos. Dans PMA Sloot, D Abramson, AV Bogdanov, YE Gorbachev, JJ Dongarra & AY Zomaya (eds), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), VOL. 2660, Springer Verlag, p. 346-354. https://doi.org/10.1007/3-540-44864-0_36

Performance evaluation of generalized polynomial chaos. / Xiu, Dongbin; Lucor, Didier; Su, C. H. et al.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Ed. / Peter M. A. Sloot; David Abramson; Alexander V. Bogdanov; Yuriy E. Gorbachev; Jack J. Dongarra; Albert Y. Zomaya. Springer Verlag, 2003. p. 346-354 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol 2660).

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Chapitre › Revue par des pairs

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N2 - In this paper we review some applications of generalized polynomial chaos expansion for uncertainty quantification. The mathematical framework is presented and the convergence of the method is demonstrated for model problems. In particular, we solve the first-order and second-order ordinary differential equations with random parameters, and examine the efficiency of generalized polynomial chaos compared to Monte Carlo simulations. It is shown that the generalized polynomial chaos can be orders of magnitude more efficient than Monte Carlo simulations when the dimensionality of random input is low, e.g. for correlated noise.

AB - In this paper we review some applications of generalized polynomial chaos expansion for uncertainty quantification. The mathematical framework is presented and the convergence of the method is demonstrated for model problems. In particular, we solve the first-order and second-order ordinary differential equations with random parameters, and examine the efficiency of generalized polynomial chaos compared to Monte Carlo simulations. It is shown that the generalized polynomial chaos can be orders of magnitude more efficient than Monte Carlo simulations when the dimensionality of random input is low, e.g. for correlated noise.

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BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Sloot, Peter M. A.

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Xiu D, Lucor D, Su CH, Karniadakis GE. Performance evaluation of generalized polynomial chaos. Dans Sloot PMA, Abramson D, Bogdanov AV, Gorbachev YE, Dongarra JJ, Zomaya AY, rédacteurs en chef, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2003. p. 346-354. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-44864-0_36

Performance evaluation of generalized polynomial chaos

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