TY - JOUR
T1 - Bayesian Model Calibration with Interpolating Polynomials Based on Adaptively Weighted Leja Nodes
AU - van den Bos , Laurent
AU - Sanderse , Benjamin
AU - Bierbooms , Wim
AU - van Bussel , Gerard
JO - Communications in Computational Physics
VL - 1
SP - 33
EP - 69
PY - 2019
DA - 2019/10
SN - 27
DO - http://doi.org/10.4208/cicp.OA-2018-0218
UR - https://global-sci.org/intro/article_detail/cicp/13313.html
KW - Bayesian model calibration, interpolation, Leja nodes, surrogate modeling.
AB - <p style="text-align: justify;">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&#39; 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&#39;
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.</p>