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PICS Colloquium: “Learning parsimonious models by covariance balancing” with Clarence Rowley
February 6 at 2:00 PM - 3:00 PM
Abstract: Data-driven reduced-order models often struggle with high-dimensional nonlinear systems sensitive to low-variance coordinates, which are typically truncated. To address this, we use ideas from balanced truncation and active subspaces to identify low-dimensional coordinate systems that balance adjoint-based sensitivity information with state variance along trajectories. Our method, analogous to balanced truncation, replaces system Gramians with state and adjoint-based gradient covariance matrices, maintaining key transformation laws. We also present a further refinement whereby the resulting oblique projection is iteratively optimized to minimize forecasting error. We demonstrate and compare these techniques with other methods on a challenging toy problem and a nonlinear axisymmetric jet flow simulation with 100,000 state variables.
Clarence Rowley
Professor of Engineering Science at Princeton University
Clancy Rowley is the Sin-I Cheng Professor of Engineering Science in the Department of Mechanical and Aerospace Engineering at Princeton, and is an associated faculty in the Program in Applied and Computational Mathematics. He received his undergraduate degree from Princeton and his doctoral degree from Caltech, both in Mechanical Engineering. He has received several awards, including an NSF CAREER Award and an AFOSR Young Investigator Award, and he is a Fellow of the American Physical Society. His research interests lie at the intersection of dynamical systems, control theory, and fluid mechanics, and focus on reduced-order models suitable for analysis and control design.