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A new surrogate modeling method combining polynomial chaos expansion and Gaussian kernel in a sparse Bayesian learning framework
Author(s) -
Zhou Yicheng,
Lu Zhenzhou,
Cheng Kai
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6145
Subject(s) - polynomial chaos , surrogate model , kriging , kernel (algebra) , parameterized complexity , mathematical optimization , bayesian optimization , gaussian process , robustness (evolution) , uncertainty quantification , computer science , algorithm , bayesian probability , mathematics , gaussian , artificial intelligence , machine learning , monte carlo method , statistics , physics , quantum mechanics , biochemistry , chemistry , combinatorics , gene
Summary Surrogate modeling techniques have been increasingly developed for optimization and uncertainty quantification problems in many engineering fields. The development of surrogates requires modeling high‐dimensional and nonsmooth functions with limited information. To this end, the hybrid surrogate modeling method, where different surrogate models are combined, offers an effective solution. In this paper, a new hybrid modeling technique is proposed by combining polynomial chaos expansion and kernel function in a sparse Bayesian learning framework. The proposed hybrid model possesses both the global characteristic advantage of polynomial chaos expansion and the local characteristic advantage of the Gaussian kernel. The parameterized priors are utilized to encourage the sparsity of the model. Moreover, an optimization algorithm aiming at maximizing Bayesian evidence is proposed for parameter optimization. To assess the performance of the proposed method, a detailed comparison is made with the well‐established PC‐Kriging technique. The results show that the proposed method is superior in terms of accuracy and robustness.