Bayesian operator inference for data-driven reduced-order modeling
(2022) In Computer Methods in Applied Mechanics and Engineering 402.- Abstract
This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian inverse problem with Gaussian prior and likelihood. The resulting posterior distribution characterizes the operators defining the reduced-order model, hence the predictions subsequently issued by the reduced-order model are endowed with uncertainty. The statistical moments of these predictions are estimated via a Monte Carlo sampling of the posterior distribution. Since the reduced models are fast to solve, this sampling is computationally efficient. Furthermore, the proposed Bayesian framework provides a... (More)
This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian inverse problem with Gaussian prior and likelihood. The resulting posterior distribution characterizes the operators defining the reduced-order model, hence the predictions subsequently issued by the reduced-order model are endowed with uncertainty. The statistical moments of these predictions are estimated via a Monte Carlo sampling of the posterior distribution. Since the reduced models are fast to solve, this sampling is computationally efficient. Furthermore, the proposed Bayesian framework provides a statistical interpretation of the regularization term that is present in the deterministic operator inference problem, and the empirical Bayes approach of maximum marginal likelihood suggests a selection algorithm for the regularization hyperparameters. The proposed method is demonstrated on two examples: the compressible Euler equations with noise-corrupted observations, and a single-injector combustion process.
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- author
- Guo, Mengwu LU ; McQuarrie, Shane A. and Willcox, Karen E.
- publishing date
- 2022-12-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Bayesian inversion, Data-driven reduced-order modeling, Operator inference, Single-injector combustion, Tikhonov regularization, Uncertainty quantification
- in
- Computer Methods in Applied Mechanics and Engineering
- volume
- 402
- article number
- 115336
- publisher
- Elsevier
- external identifiers
-
- scopus:85134808819
- ISSN
- 0045-7825
- DOI
- 10.1016/j.cma.2022.115336
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2022 The Author(s)
- id
- 9b930325-07ba-4028-b746-3832806bbb3d
- date added to LUP
- 2024-03-19 12:26:31
- date last changed
- 2024-04-17 14:19:45
@article{9b930325-07ba-4028-b746-3832806bbb3d,
abstract = {{<p>This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian inverse problem with Gaussian prior and likelihood. The resulting posterior distribution characterizes the operators defining the reduced-order model, hence the predictions subsequently issued by the reduced-order model are endowed with uncertainty. The statistical moments of these predictions are estimated via a Monte Carlo sampling of the posterior distribution. Since the reduced models are fast to solve, this sampling is computationally efficient. Furthermore, the proposed Bayesian framework provides a statistical interpretation of the regularization term that is present in the deterministic operator inference problem, and the empirical Bayes approach of maximum marginal likelihood suggests a selection algorithm for the regularization hyperparameters. The proposed method is demonstrated on two examples: the compressible Euler equations with noise-corrupted observations, and a single-injector combustion process.</p>}},
author = {{Guo, Mengwu and McQuarrie, Shane A. and Willcox, Karen E.}},
issn = {{0045-7825}},
keywords = {{Bayesian inversion; Data-driven reduced-order modeling; Operator inference; Single-injector combustion; Tikhonov regularization; Uncertainty quantification}},
language = {{eng}},
month = {{12}},
publisher = {{Elsevier}},
series = {{Computer Methods in Applied Mechanics and Engineering}},
title = {{Bayesian operator inference for data-driven reduced-order modeling}},
url = {{http://dx.doi.org/10.1016/j.cma.2022.115336}},
doi = {{10.1016/j.cma.2022.115336}},
volume = {{402}},
year = {{2022}},
}