Thursday, March 30, 2023 03:00PM

You're invited to attend


“Learning Dynamics of Nonlinear Systems 
via Structure-Preserving Operator Inference”




Boris Kramer 
Assistant Professor | Mechanical and Aerospace Engineering 
University of California San Diego



Thursday, March 30
3 - 4 p.m.
Student Success Center Press Room A



About the Seminar
In this talk, we will discuss several extensions of a data-driven structure-preserving model reduction framework via operator inference. We will illustrate how that framework learns reduced-order models non-intrusively, and how additional knowledge—which is often present about fluid dynamical and other mechanical systems—can be embedded as constraints for the resulting optimization problem. Three aspects will be discussed: First, we will present variable transformations to turn highly nonlinear models into quadratic form, which can then be straightforwardly parametrized and learned. We will illustrate the results on a 2d rocket combustion application. Second, for energy-preserving systems, we will embed Hamiltonian structure into the model learning framework, which guarantees that the learned models are long-term stable and energy-conserving. We will illustrate those results on a wave equation and the nonlinear Schroedinger equation. Lastly, we present recent results for stability-domain estimates for quadratic systems, and how those can be used to regularize the learning problem to guarantee stable models, illustrated on the quadratic Burgers’ equation.

About the Speaker
Boris Kramer is an Assistant Professor in Mechanical and Aerospace Engineering at the University of California San Diego. Prior to joining UC San Diego, he spent four years as a Postdoctoral Associate in the department of Aeronautics and Astronautics and the Aerospace Computational Design Lab (ACDL) at the Massachusetts Institute of Technology (MIT). He received his M.Sc. (2011) and Ph.D. (2015) in Mathematics from Virginia Tech. Prior to that, he studied Mathematics in Technology and Mechanical Engineering at the University of Karlsruhe (now KIT), Germany. He is a member of the Society for Industrial and Applied Mathematics (SIAM), and a Senior Member of AIAA where he also serves on the Multidisciplinary Design Optimization and Nondeterministic Approaches Technical Committees. He is a 2022 NSF CAREER Awardee and won a DoD Newton Award in 2020. His research is funded by the Office of Naval Research (ONR), the Defense Advanced Research Projects Agency (DARPA) and the National Science Foundation. His research interests are to develop computational methods and numerical analysis for control, optimization, design and uncertainty quantification of complex and large-scale systems.