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

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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.

Original language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Peter M. A. Sloot, David Abramson, Alexander V. Bogdanov, Yuriy E. Gorbachev, Jack J. Dongarra, Albert Y. Zomaya
Publisher	Springer Verlag
Pages	346-354
Number of pages	9
ISBN (Print)	3540401970, 9783540401971
DOIs	https://doi.org/10.1007/3-540-44864-0_36
Publication status	Published - 1 Jan 2003
Externally published	Yes

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2660
ISSN (Print)	0302-9743
ISSN (Electronic)	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. In 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) (pp. 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). editor / Peter M. A. Sloot ; David Abramson ; Alexander V. Bogdanov ; Yuriy E. Gorbachev ; Jack J. Dongarra ; Albert Y. Zomaya. Springer Verlag, 2003. pp. 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",

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language = "English",

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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. in 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, pp. 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).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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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. In Sloot PMA, Abramson D, Bogdanov AV, Gorbachev YE, Dongarra JJ, Zomaya AY, editors, 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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