Bayesian Uncertainty Quantification for Functional Response

Chunlin Ji, Xiao Guo, Yang He, Binbin Zhu, Yang Yang, Ke Deng and Ruopeng Liu

A chapter in Uncertainty Quantification and Model Calibration from IntechOpen

Abstract: This chapter addresses the stochastic modeling of functional response, which is a major concern in engineering implementation. We first introduce a general framework and several conventional models for functional data, including the functional linear model, penalized regression splines, and the spatial temporal model. However, in engineering practice, a naive mathematical modeling of functional response may fail due to the lack of expressing the underlying physical mechanism. We propose a series of quasiphysical models to handle the functional response. A motivating example of metamaterial design is thoroughly discussed to demonstrate the idea of quasiphysical models. In real applications, various uncertainties have to be taken into account, such as that of the permittivity or permeability of the substrate of the metamaterial. For the propagation of uncertainty, simulation-based methods are discussed. A Bayesian framework is presented to deal with the model calibration in the case of functional response. Experimental results illustrate the efficiency of the proposed method.

Keywords: functional response; meta model; Bayesian uncertainty quantification; model calibration; metamaterial design (search for similar items in EconPapers)
JEL-codes: C10 (search for similar items in EconPapers)
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Persistent link: https://EconPapers.repec.org/RePEc:ito:pchaps:114339

DOI: 10.5772/intechopen.69385

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