期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 402, 期 -, 页码 -出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2022.115336
关键词
Data-driven reduced-order modeling; Uncertainty quantification; Operator inference; Bayesian inversion; Tikhonov regularization; Single-injector combustion
资金
- ARPA-E DIFFERENTIATE Program [DE-AR0001208]
- U.S. Department of Energy, National Nuclear Security Administration [DE-NA0003969]
- U.S. Department of Energy AEOLUS MMICC center [DE-SC0019303]
- Air Force Center of Excellence on Multi -Fidelity Modeling of Rocket Combustor Dynamics (Air Force Office of Scientific Research) [FA9550-17-1-0195]
- Sectorplan Beta (the Netherlands) under the focus area Mathematics of Computational Science
- U.S. Department of Energy (DOE) [DE-SC0019303] Funding Source: U.S. Department of Energy (DOE)
This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. The study formulates the task of learning a reduced-order model as a Bayesian inverse problem, with a Gaussian prior and likelihood. The resulting posterior distribution characterizes the operators defining the reduced-order model, enabling predictions with uncertainty. The method estimates statistical moments of the predictions through efficient Monte Carlo sampling.
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.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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