An efficient surrogate modeling approach in Bayesian uncertainty analysis

Guannan Zhang; Dan Lu; Ming Ye; Max Gunzburger; Clayton Webster

doi:10.1063/1.4825643

An efficient surrogate modeling approach in Bayesian uncertainty analysis

Guannan Zhang, Dan Lu, Ming Ye, Max Gunzburger, Clayton Webster

Data Analysis and Machine Learning

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

Abstract

We develop an efficient sparse-grid Bayesian approach for quantifying parametric and predictive uncertainties of physical systems constrained by stochastic PDEs. An accurate surrogate posterior distribution is constructed using sparse-grid interpolation and integration. It improves the simulation efficiency by accelerating the evaluation of the posterior distribution without losing much accuracy, and by determining an appropriate importance density for importance sampling which is easily sampled and captures the main features of the exact posterior distribution.

Original language	English
Title of host publication	11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013
Pages	898-901
Number of pages	4
DOIs	https://doi.org/10.1063/1.4825643
State	Published - 2013
Event	11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013 - Rhodes, Greece Duration: Sep 21 2013 → Sep 27 2013

Publication series

Name	AIP Conference Proceedings
Volume	1558
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013
Country/Territory	Greece
City	Rhodes
Period	09/21/13 → 09/27/13

Keywords

Bayesian inference
Uncertainty quantification
importance sampling
sparse grids

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10.1063/1.4825643

Cite this

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title = "An efficient surrogate modeling approach in Bayesian uncertainty analysis",

abstract = "We develop an efficient sparse-grid Bayesian approach for quantifying parametric and predictive uncertainties of physical systems constrained by stochastic PDEs. An accurate surrogate posterior distribution is constructed using sparse-grid interpolation and integration. It improves the simulation efficiency by accelerating the evaluation of the posterior distribution without losing much accuracy, and by determining an appropriate importance density for importance sampling which is easily sampled and captures the main features of the exact posterior distribution.",

keywords = "Bayesian inference, Uncertainty quantification, importance sampling, sparse grids",

author = "Guannan Zhang and Dan Lu and Ming Ye and Max Gunzburger and Clayton Webster",

year = "2013",

doi = "10.1063/1.4825643",

language = "English",

isbn = "9780735411845",

series = "AIP Conference Proceedings",

pages = "898--901",

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note = "11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013 ; Conference date: 21-09-2013 Through 27-09-2013",

}

Zhang, G , Lu, D, Ye, M, Gunzburger, M & Webster, C 2013, An efficient surrogate modeling approach in Bayesian uncertainty analysis. in 11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013. AIP Conference Proceedings, vol. 1558, pp. 898-901, 11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013, Rhodes, Greece, 09/21/13. https://doi.org/10.1063/1.4825643

An efficient surrogate modeling approach in Bayesian uncertainty analysis. / Zhang, Guannan ; Lu, Dan; Ye, Ming et al.
11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013. 2013. p. 898-901 (AIP Conference Proceedings; Vol. 1558).

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

TY - GEN

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AU - Zhang, Guannan

AU - Lu, Dan

AU - Ye, Ming

AU - Gunzburger, Max

AU - Webster, Clayton

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N2 - We develop an efficient sparse-grid Bayesian approach for quantifying parametric and predictive uncertainties of physical systems constrained by stochastic PDEs. An accurate surrogate posterior distribution is constructed using sparse-grid interpolation and integration. It improves the simulation efficiency by accelerating the evaluation of the posterior distribution without losing much accuracy, and by determining an appropriate importance density for importance sampling which is easily sampled and captures the main features of the exact posterior distribution.

AB - We develop an efficient sparse-grid Bayesian approach for quantifying parametric and predictive uncertainties of physical systems constrained by stochastic PDEs. An accurate surrogate posterior distribution is constructed using sparse-grid interpolation and integration. It improves the simulation efficiency by accelerating the evaluation of the posterior distribution without losing much accuracy, and by determining an appropriate importance density for importance sampling which is easily sampled and captures the main features of the exact posterior distribution.

KW - Bayesian inference

KW - Uncertainty quantification

KW - importance sampling

KW - sparse grids

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DO - 10.1063/1.4825643

M3 - Conference contribution

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T3 - AIP Conference Proceedings

SP - 898

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BT - 11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013

T2 - 11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013

Y2 - 21 September 2013 through 27 September 2013

ER -

An efficient surrogate modeling approach in Bayesian uncertainty analysis

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