February 3, 2022  – The Mezić Group pleased to host Petar Bevanda from Technical University of Munich

A recording of the talk is on our Youtube channel.

Petar Bevanda from Technical University of Munich, Germany will give a Zoom seminar on Thursday, February 3, 2022 at 9AM PST.

Title: KoopmanizingFlows: Diffeomorphically Learning Stable Koopman Operators

Abstract: Global linearization methods for nonlinear systems inspired by the infinite-dimensional, linear Koopman operator have received increased attention for data-driven modeling of nonlinear dynamics in recent years. By lifting a finite-dimensional nonlinear system to a higher-dimensional linear operator representation, superior complexity-accuracy balance compared to conventional nonlinear modeling is possible through the use of efficient linear techniques for prediction, analysis and control. Learning meaningful finite-dimensional representations of Koopman operators presents a challenging problem, as one needs to learn linear time-invariant (LTI) features that are both Koopman-invariant (evolve linearly under the dynamics) as well as relevant (spanning the original state) - a generally unsupervised learning task. For a structured solution to this unsupervised problem, we propose learning Koopman-invariant coordinates by composing a lifted aggregate system of a latent linear model with a diffeomorphic learner based on Normalizing Flows. Using an unconstrained parameterization of stable matrices along with the aforementioned feature construction, we learn the Koopman operator features without assuming a predefined library of functions or knowing the spectrum, while ensuring stability regardless of the operator approximation accuracy – resulting in the KoopmanizingFlow Stable Dynamical Systems (KF-SDS) framework. We demonstrate the superior efficacy of the proposed method in comparison to a state-of-the-art method on the well-known LASA handwriting dataset. This talk is based on the following preprint of ours https://arxiv.org/pdf/2112.04085.pdf.

Short Bio: Petar Bevanda is PhD student at the Technical University of Munich (TUM). He received his M.Sc. degree in Electrical and Computer Engineering at the Technical University of Munich in 2020. Beginning of 2021, he began pursuing his PhD degree at the Chair of Information-oriented Control in the Department of Electrical and Computer Engineering at Technical University of Munich. His research interests include data-driven modeling based on linear evolution operators, model predictive control and safe learning.