Adaptive surrogate modeling for response surface approximations with application to bayesian inference

Serge Prudhomme; Corey M. Bryant

doi:10.1186/s40323-015-0045-5

Adaptive surrogate modeling for response surface approximations with application to bayesian inference

Serge Prudhomme, Corey M. Bryant

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Parameter estimation for complex models using Bayesian inference is usually a very costly process as it requires a large number of solves of the forward problem. We show here how the construction of adaptive surrogate models using a posteriori error estimates for quantities of interest can significantly reduce the computational cost in problems of statistical inference. As surrogate models provide only approximations of the true solutions of the forward problem, it is nevertheless necessary to control these errors in order to construct an accurate reduced model with respect to the observables utilized in the identification of the model parameters. Effectiveness of the proposed approach is demonstrated on a numerical example dealing with the Spalart–Allmaras model for the simulation of turbulent channel flows. In particular, we illustrate how Bayesian model selection using the adapted surrogate model in place of solving the coupled nonlinear equations leads to the same quality of results while requiring fewer nonlinear PDE solves.

Original language	English (US)
Journal	Advanced Modeling and Simulation in Engineering Sciences
Volume	2
Issue number	1
DOIs	https://doi.org/10.1186/s40323-015-0045-5
State	Published - Sep 17 2015
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: SP is grateful for the support by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. He is also a participant of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering. CB acknowledges the support by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615]. The authors are also grateful to Todd Oliver from the Institute for Computational Engineering and Sciences at The University of Texas at Austin for useful discussions on the Spalart–Allmaras model and the calibration of the model parameters using Bayesian inference.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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title = "Adaptive surrogate modeling for response surface approximations with application to bayesian inference",

abstract = "Parameter estimation for complex models using Bayesian inference is usually a very costly process as it requires a large number of solves of the forward problem. We show here how the construction of adaptive surrogate models using a posteriori error estimates for quantities of interest can significantly reduce the computational cost in problems of statistical inference. As surrogate models provide only approximations of the true solutions of the forward problem, it is nevertheless necessary to control these errors in order to construct an accurate reduced model with respect to the observables utilized in the identification of the model parameters. Effectiveness of the proposed approach is demonstrated on a numerical example dealing with the Spalart–Allmaras model for the simulation of turbulent channel flows. In particular, we illustrate how Bayesian model selection using the adapted surrogate model in place of solving the coupled nonlinear equations leads to the same quality of results while requiring fewer nonlinear PDE solves.",

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note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: SP is grateful for the support by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. He is also a participant of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering. CB acknowledges the support by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615]. The authors are also grateful to Todd Oliver from the Institute for Computational Engineering and Sciences at The University of Texas at Austin for useful discussions on the Spalart–Allmaras model and the calibration of the model parameters using Bayesian inference. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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N2 - Parameter estimation for complex models using Bayesian inference is usually a very costly process as it requires a large number of solves of the forward problem. We show here how the construction of adaptive surrogate models using a posteriori error estimates for quantities of interest can significantly reduce the computational cost in problems of statistical inference. As surrogate models provide only approximations of the true solutions of the forward problem, it is nevertheless necessary to control these errors in order to construct an accurate reduced model with respect to the observables utilized in the identification of the model parameters. Effectiveness of the proposed approach is demonstrated on a numerical example dealing with the Spalart–Allmaras model for the simulation of turbulent channel flows. In particular, we illustrate how Bayesian model selection using the adapted surrogate model in place of solving the coupled nonlinear equations leads to the same quality of results while requiring fewer nonlinear PDE solves.

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Adaptive surrogate modeling for response surface approximations with application to bayesian inference

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