Sampling-based adaptive Bayesian quadrature for probabilistic model updating

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  • Northwestern Polytechnical University
  • University of Liverpool
  • Tongji University
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Original languageEnglish
Article number117467
JournalComputer Methods in Applied Mechanics and Engineering
Volume433
Issue numberPart A
Early online date25 Oct 2024
Publication statusE-pub ahead of print - 25 Oct 2024

Abstract

Bayesian (probabilistic) model updating is a fundamental concept in computational science, allowing for the incorporation of prior beliefs with observed data to reduce prediction uncertainty of a computer simulator. However, the efficient evaluation of posterior probability density functions (PDFs) of model parameters poses challenges, particularly for computationally expansive simulators. This work presents a sampling-based adaptive Bayesian quadrature method to fill this gap. The method is based on approximating the simulator under investigation with a Gaussian process (GP) model, and then a conditional sampling procedure is introduced for generating sample paths, this way to infer a probability distribution for the evidence term. This inferred probability distribution indeed measures the prediction uncertainty of the evidence term, and thus based on which, an acquisition function is proposed to identify the site at which the prediction uncertainty of the GP model contributes the most to that of the evidence term. All the above ingredients finally form an adaptive algorithm for updating the posterior PDFs of model parameters with pre-specified accuracy tolerance. Case studies across numerical examples and engineering applications validate the ability of the proposed method to deal with multi-modal problems, and demonstrate its superiority in terms of computational efficiency and precision for estimating model evidence and posterior PDFs.

Keywords

    Active learning, Bayesian quadrature, Gaussian process, Inverse problem, Stochastic updating

ASJC Scopus subject areas

Cite this

Sampling-based adaptive Bayesian quadrature for probabilistic model updating. / Song, Jingwen; Liang, Zhanhua; Wei, Pengfei et al.
In: Computer Methods in Applied Mechanics and Engineering, Vol. 433, No. Part A, 117467, 01.01.2025.

Research output: Contribution to journalArticleResearchpeer review

Song J, Liang Z, Wei P, Beer M. Sampling-based adaptive Bayesian quadrature for probabilistic model updating. Computer Methods in Applied Mechanics and Engineering. 2025 Jan 1;433(Part A):117467. Epub 2024 Oct 25. doi: 10.1016/j.cma.2024.117467
Song, Jingwen ; Liang, Zhanhua ; Wei, Pengfei et al. / Sampling-based adaptive Bayesian quadrature for probabilistic model updating. In: Computer Methods in Applied Mechanics and Engineering. 2025 ; Vol. 433, No. Part A.
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