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

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    Type
    Article
    Authors
    Prudhomme, Serge
    Bryant, Corey M.
    Date
    2015-09-17
    Online Publication Date
    2015-09-17
    Print Publication Date
    2015-12
    Permanent link to this record
    http://hdl.handle.net/10754/597461
    
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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.
    Citation
    Prudhomme S, Bryant CM (2015) Adaptive surrogate modeling for response surface approximations with application to bayesian inference. Advanced Modeling and Simulation in Engineering Sciences 2. Available: http://dx.doi.org/10.1186/s40323-015-0045-5.
    Sponsors
    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.
    Publisher
    Springer Nature
    Journal
    Advanced Modeling and Simulation in Engineering Sciences
    DOI
    10.1186/s40323-015-0045-5
    ae974a485f413a2113503eed53cd6c53
    10.1186/s40323-015-0045-5
    Scopus Count
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    Publications Acknowledging KAUST Support

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