Multielement polynomial chaos Kriging-based metamodelling for Bayesian inference of non-smooth systems

• URL: http://arxiv.org/abs/2212.02250v1
• Date: Mon, 5 Dec 2022 13:22:39 GMT
• Title: Multielement polynomial chaos Kriging-based metamodelling for Bayesian inference of non-smooth systems
• Authors: J.C. Garc\'ia-Merino, C. Calvo-Jurado, E. Mart\'inez-Pa\~neda, E. Garc\'ia-Mac\'ias
• Abstract summary: This paper presents a surrogate modelling technique based on domain partitioning for Bayesian parameter inference of highly nonlinear engineering models. The developed surrogate model combines in a piecewise function an array of local Polynomial Chaos based Kriging metamodels constructed on a finite set of non-overlapping of the input space. The efficiency and accuracy of the proposed approach are validated through two case studies, including an analytical benchmark and a numerical case study.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper presents a surrogate modelling technique based on domain partitioning for Bayesian parameter inference of highly nonlinear engineering models. In order to alleviate the computational burden typically involved in Bayesian inference applications, a multielement Polynomial Chaos Expansion based Kriging metamodel is proposed. The developed surrogate model combines in a piecewise function an array of local Polynomial Chaos based Kriging metamodels constructed on a finite set of non-overlapping subdomains of the stochastic input space. Therewith, the presence of non-smoothness in the response of the forward model (e.g.~ nonlinearities and sparseness) can be reproduced by the proposed metamodel with minimum computational costs owing to its local adaptation capabilities. The model parameter inference is conducted through a Markov chain Monte Carlo approach comprising adaptive exploration and delayed rejection. The efficiency and accuracy of the proposed approach are validated through two case studies, including an analytical benchmark and a numerical case study. The latter relates the partial differential equation governing the hydrogen diffusion phenomenon of metallic materials in Thermal Desorption Spectroscopy tests.

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