Combining data and physical models for probabilistic analysis: A Bayesian Augmented Space Learning perspective

Research output: Contribution to journalArticleResearchpeer review

Authors

  • Fangqi Hong
  • Pengfei Wei
  • Jingwen Song
  • Matthias G.R. Faes
  • Marcos A. Valdebenito
  • Michael Beer

Research Organisations

External Research Organisations

  • Northwestern Polytechnical University
  • TU Dortmund University
  • University of Liverpool
  • International Joint Research Center for Engineering Reliability and Stochastic Mechanics
  • Tongji University
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Details

Original languageEnglish
Article number103474
JournalProbabilistic Engineering Mechanics
Volume73
Publication statusPublished - Jul 2023

Abstract

The traditional methods for probabilistic analysis of physical systems often follow a non-intrusive scheme with, random samples for stochastic model parameters generated in the outer loop, and for each sample, physical model (described by PDEs) solved in the inner loop using, e.g., finite element method (FEM). Two of the biggest challenges when applying probabilistic methods are the high computational burden due to the repeated calls of the expensive-to-estimate computational models, and the difficulties of integrating the numerical errors from both loops. To overcome these challenges, we present a new framework for transforming the PDEs with stochastic parameters into equivalent deterministic PDEs, and then devise a statistical inference method, called Bayesian Augmented Space Learning (BASL), for inferring the probabilistic descriptors of the model responses with the combination of measurement data and physical models. With the two sources of information available, only a one-step Bayesian inference needs to be performed, and the numerical errors are summarized by posterior variances. The method is then further extended to the case where the values of the parameters of the test pieces for measurement are not precisely known. The effectiveness of the proposed methods is demonstrated with academic and real-world physical models.

Keywords

    Augmented space, Bayesian learning, Gaussian process regression, Parameter identification, Probabilistic analysis

ASJC Scopus subject areas

Cite this

Combining data and physical models for probabilistic analysis: A Bayesian Augmented Space Learning perspective. / Hong, Fangqi; Wei, Pengfei; Song, Jingwen et al.
In: Probabilistic Engineering Mechanics, Vol. 73, 103474, 07.2023.

Research output: Contribution to journalArticleResearchpeer review

Hong F, Wei P, Song J, Faes MGR, Valdebenito MA, Beer M. Combining data and physical models for probabilistic analysis: A Bayesian Augmented Space Learning perspective. Probabilistic Engineering Mechanics. 2023 Jul;73:103474. doi: 10.1016/j.probengmech.2023.103474
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abstract = "The traditional methods for probabilistic analysis of physical systems often follow a non-intrusive scheme with, random samples for stochastic model parameters generated in the outer loop, and for each sample, physical model (described by PDEs) solved in the inner loop using, e.g., finite element method (FEM). Two of the biggest challenges when applying probabilistic methods are the high computational burden due to the repeated calls of the expensive-to-estimate computational models, and the difficulties of integrating the numerical errors from both loops. To overcome these challenges, we present a new framework for transforming the PDEs with stochastic parameters into equivalent deterministic PDEs, and then devise a statistical inference method, called Bayesian Augmented Space Learning (BASL), for inferring the probabilistic descriptors of the model responses with the combination of measurement data and physical models. With the two sources of information available, only a one-step Bayesian inference needs to be performed, and the numerical errors are summarized by posterior variances. The method is then further extended to the case where the values of the parameters of the test pieces for measurement are not precisely known. The effectiveness of the proposed methods is demonstrated with academic and real-world physical models.",
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note = "Funding Information: Pengfei Wei acknowledges the supports of the National Natural Science Foundation of China under grant number 72171194 and the Sino-German Mobility Programme under grant number M-0175 (2021–2023). Matthias Faes acknowledges the support of the Research Foundation Flanders (FWO), Belgium under grant 12P3519N , as well as of the Humboldt foundation.",
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T2 - A Bayesian Augmented Space Learning perspective

AU - Hong, Fangqi

AU - Wei, Pengfei

AU - Song, Jingwen

AU - Faes, Matthias G.R.

AU - Valdebenito, Marcos A.

AU - Beer, Michael

N1 - Funding Information: Pengfei Wei acknowledges the supports of the National Natural Science Foundation of China under grant number 72171194 and the Sino-German Mobility Programme under grant number M-0175 (2021–2023). Matthias Faes acknowledges the support of the Research Foundation Flanders (FWO), Belgium under grant 12P3519N , as well as of the Humboldt foundation.

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N2 - The traditional methods for probabilistic analysis of physical systems often follow a non-intrusive scheme with, random samples for stochastic model parameters generated in the outer loop, and for each sample, physical model (described by PDEs) solved in the inner loop using, e.g., finite element method (FEM). Two of the biggest challenges when applying probabilistic methods are the high computational burden due to the repeated calls of the expensive-to-estimate computational models, and the difficulties of integrating the numerical errors from both loops. To overcome these challenges, we present a new framework for transforming the PDEs with stochastic parameters into equivalent deterministic PDEs, and then devise a statistical inference method, called Bayesian Augmented Space Learning (BASL), for inferring the probabilistic descriptors of the model responses with the combination of measurement data and physical models. With the two sources of information available, only a one-step Bayesian inference needs to be performed, and the numerical errors are summarized by posterior variances. The method is then further extended to the case where the values of the parameters of the test pieces for measurement are not precisely known. The effectiveness of the proposed methods is demonstrated with academic and real-world physical models.

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