Mengwu Guo, Mathematics, Lund University Title: Bayesian learning for low-dimensional representations of time-dependent nonlinear systems

Abstract. Credible real-time simulation is a critical enabling factor for digital twin technology, and data-driven model reduction is a natural choice for achieving it. In this talk, we will discuss a probabilistic strategy for the learning of reduced-order representations of high-dimensional dynamical systems, with which a significantly reduced dimensionality guarantees improved efficiency, and the facilitated uncertainty quantification certifies computational reliability. The strategy is based on Bayesian reduced-order operator inference, a data-driven method that inherits the formulation structure of projection-based reduced-state governing equations yet without requiring access to full-order solvers. The reduced-order operators are estimated using Bayesian inference. Two different strategies of likelihood definition will be discussed – one formulated as linear regression, and the other through Gaussian processes. In particular, the latter aims to improve the predictive performance of the resulting reduced models when training data are noisy and/or scarce. The estimated reduced-order operators probabilistically define a low-dimensional dynamical system for the predominant latent states, and provide an inherently embedded regularization together with the quantification of modeling uncertainties.