@article{93e8a0af79a849dc987ddfba2e35c3b9,
title = "Bayesian operator inference for data-driven reduced-order modeling",
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 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.",
keywords = "UT-Hybrid-D",
author = "Mengwu Guo and McQuarrie, {Shane A.} and Willcox, {Karen E.}",
year = "2022",
month = dec,
day = "1",
doi = "10.1016/j.cma.2022.115336",
language = "English",
volume = "402",
journal = "Computer methods in applied mechanics and engineering",
issn = "0045-7825",
publisher = "Elsevier B.V.",
}