Print Email Facebook Twitter Bayesian model calibration with interpolating polynomials based on adaptively weighted leja nodes Title Bayesian model calibration with interpolating polynomials based on adaptively weighted leja nodes Author van den Bos, L.M.M. (TU Delft Wind Energy; Centrum Wiskunde & Informatica (CWI)) Sanderse, Benjamin (Centrum Wiskunde & Informatica (CWI)) Bierbooms, W.A.A.M. (TU Delft Wind Energy) van Bussel, G.J.W. (TU Delft Wind Energy) Date 2020 Abstract An efficient algorithm is proposed for Bayesian model calibration, which is commonly used to estimate the model parameters of non-linear, computationally expensive models using measurement data. The approach is based on Bayesian statistics: using a prior distribution and a likelihood, the posterior distribution is obtained through application of Bayes' law. Our novel algorithm to accurately determine this posterior requires significantly fewer discrete model evaluations than traditional Monte Carlo methods. The key idea is to replace the expensive model by an interpolating surrogate model and to construct the interpolating nodal set maximizing the accuracy of the posterior. To determine such a nodal set an extension to weighted Leja nodes is introduced, based on a new weighting function. We prove that the convergence of the posterior has the same rate as the convergence of the model. If the convergence of the posterior is measured in the Kullback-Leibler divergence, the rate doubles. The algorithm and its theoretical properties are verified in three different test cases: analytical cases that confirm the correctness of the theoretical findings, Burgers' equation to show its applicability in implicit problems, and finally the calibration of the closure parameters of a turbulence model to show the effectiveness for computationally expensive problems. Subject Bayesian model calibrationInterpolationLeja nodesSurrogate modelinginterpolationsurrogate modeling To reference this document use: http://resolver.tudelft.nl/uuid:1b0a6714-bf62-4d51-9980-2f1d31c8a62d DOI https://doi.org/10.4208/cicp.OA-2018-0218 ISSN 1815-2406 Source Communications in Computational Physics, 27 (1), 33-69 Bibliographical note accepted author manuscript Part of collection Institutional Repository Document type journal article Rights © 2020 L.M.M. van den Bos, Benjamin Sanderse, W.A.A.M. Bierbooms, G.J.W. van Bussel Files PDF 1802.02035.pdf 3.79 MB Close viewer /islandora/object/uuid:1b0a6714-bf62-4d51-9980-2f1d31c8a62d/datastream/OBJ/view