90 Adaptive Response Surface Approximation Method for Bayesian Inference - ADMOS 2015 - Serge Prudhomme* and Corey M. Bryant† * Department of Mathematics and Industrial Engineering Ecole Polytechnique de Montréal C.P. 6079, succ. Centre-Ville, Montréal QC H3C 3A7, Canada e-mail:
[email protected] † Institute for Computational Engineering and Sciences The University of Texas at Austin Austin, TX 78712, USA Email: [email protected] ABSTRACT The need for surrogate models and adaptive methods can be best appreciated if one is interested in parameter estimation using a Bayesian calibration procedure for validation purposes [1,2]. We extend our work on error decomposition and adaptive refinement for response surfaces [3] to the development of a surrogate model that can be utilized to estimate the parameters of Reynoldsaveraged Navier-Stokes models. The error estimates and adaptive schemes are driven here by a quantity of interest and are thus based on the approximation of an adjoint problem. The desired tolerance in the error of the posterior distribution allows one to establish a threshold for the accuracy of the surrogate model. Particular focus is paid to accurate estimation of evidences to facilitate model selection. REFERENCES [1] M. Panesi, K. Miki, S. Prudhomme, and A. Brandis, On the assessment of a Bayesian validation methodology for data reduction models relevant to shock tube experiments, Computer Methods in Applied Mechanics and Engineering, Vol. 213–216, pp. 383–398, (2012). [2] R. Morrison, C. Bryant, G. Terejanu, S. Prudhomme, and K. Miki, Data partition methodology for validation of predictive models, Computer & Mathematics with Applications, Vol. 66, pp. 2114–2125, (2013). [3] C.M. Bryant, S. Prudhomme, and T. Wildey, “A posteriori error control for partial differential equations with random data”, SIAM Journal on Uncertainty Quantification, Submitted (2013). Available as ICES Report 13-08, 2013. Adaptive Response Surface Approximation Method for Bayesian Inference
