Model Reduction via Optimization of Projection Operators and Reduced-Order Dynamics

Explore a cutting-edge approach to computing reduced-order models using non-intrusive methods in this hour-long talk by Alberto Padovan from the University of Illinois Urbana-Champaign. Delve into the challenges of obtaining accurate data-driven models for systems with large-amplitude transient growth and learn about a novel non-intrusive framework that simultaneously identifies oblique projection operators and reduced-order dynamics directly from data. Discover how this method optimizes over a product manifold of Grassmann and Stiefel manifolds, along with linear spaces, to fit reduced-order models of polynomial form. Compare this innovative approach with state-of-the-art techniques through three examples: a three-dimensional ODE system, the complex Ginzburg-Landau equation, and a two-dimensional lid-driven cavity flow at Reynolds number 8300. Gain insights into the intersection of fluid mechanics, dynamical systems, and control theory, with applications in model reduction of fluid flows and analysis of supersonic and hypersonic wall-bounded flows.