Mengwu Guo: Probabilistic Learning for Compact Dynamical Representations of Nonlinear Systems

Abstract:

Credible real-time simulation is a crucial enabler for digital twin technology, and data-driven model reduction is a key approach to achieving this. In this talk, we will discuss non-intrusive Bayesian methods for learning reduced-order representations of high-dimensional dynamical systems, with built-in quantification of modeling uncertainties to certify computational reliability. The core strategy involves using Bayesian inference for the parametrization inspired by projection-based model reduction. Recently, we developed a novel method that leverages Gaussian process approximations to formulate differential-equation-constrained likelihood functions and hence improve predictive performance, particularly when training data are noisy and/or scarce. This technique has demonstrated its effectiveness in data-driven reduced-order modeling by delivering accurate temporal predictions along with robust uncertainty quantification.