Adaptive surrogate modeling for response surface approximations with application to bayesian inference
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AbstractParameter 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.
CitationPrudhomme 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.
SponsorsSP 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.