Details
| Original language | English |
|---|---|
| Article number | 117467 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 433 |
| Issue number | Part A |
| Early online date | 25 Oct 2024 |
| Publication status | E-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
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 433, No. Part A, 117467, 01.01.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Sampling-based adaptive Bayesian quadrature for probabilistic model updating
AU - Song, Jingwen
AU - Liang, Zhanhua
AU - Wei, Pengfei
AU - Beer, Michael
N1 - Publisher Copyright: © 2024 Elsevier B.V.
PY - 2024/10/25
Y1 - 2024/10/25
N2 - 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.
AB - 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.
KW - Active learning
KW - Bayesian quadrature
KW - Gaussian process
KW - Inverse problem
KW - Stochastic updating
UR - http://www.scopus.com/inward/record.url?scp=85207027876&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2024.117467
DO - 10.1016/j.cma.2024.117467
M3 - Article
AN - SCOPUS:85207027876
VL - 433
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
IS - Part A
M1 - 117467
ER -