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

Serge Prudhomme et Corey M. Bryant

Article de revue (2015)

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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

Mots clés

Goal-oriented error estimation; Adjoint problem; Turbulence modeling; Spalart–Allmaras model; Parameter identification

Sujet(s): 2950 Mathématiques appliquées > 2960 Modélisation mathématique
Département: Département de mathématiques et de génie industriel
Organismes subventionnaires: CRSNG/NSERC, KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering, Department of Energy [National Nuclear Security Administration]
Numéro de subvention: DE-FC52-08NA28615
URL de PolyPublie: https://publications.polymtl.ca/5097/
Titre de la revue: Advanced Modeling and Simulation in Engineering Sciences (vol. 2, no 1)
Maison d'édition: Springer
DOI: 10.1186/s40323-015-0045-5
URL officielle: https://doi.org/10.1186/s40323-015-0045-5
Date du dépôt: 16 févr. 2023 15:18
Dernière modification: 11 mai 2023 20:25
Citer en APA 7: Prudhomme, S., & Bryant, C. M. (2015). Adaptive surrogate modeling for response surface approximations with application to bayesian inference. Advanced Modeling and Simulation in Engineering Sciences, 2(1), 22. https://doi.org/10.1186/s40323-015-0045-5

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