Bayesian operator inference for data-driven reduced-order modeling

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by structure governing equations, task learning model from data is posed as inverse problem with Gaussian prior and likelihood. The resulting posterior distribution characterizes operators defining model, hence predictions subsequently issued are endowed uncertainty. statistical moments these estimated via Monte Carlo sampling distribution. Since reduced models fast to solve, this computationally efficient. Furthermore, proposed framework provides interpretation regularization term that present in deterministic operator problem, empirical Bayes approach maximum marginal likelihood suggests selection algorithm hyperparameters. demonstrated on two examples: compressible Euler equations noise-corrupted observations, single-injector combustion process.