Pre-Conference Course: Equation- and Data-Driven Nonlinear Model Reduction for Solids, Fluids and Control

Standing on the Shoulders of Giants
Rosen Plaza Hotel, Orlando, FL  |  January 29–February 1, 2024

Equation- and Data-Driven Nonlinear Model Reduction for Solids, Fluids and Control

Sunday, January 28, 2024 | 9:00 a.m. - 6:00 p.m.

The mechanical systems arising in contemporary science and engineering are growing ever more complex. As a result, the governing equations of these processes are becoming high-dimensional or even unknown. In the latter case, only data-driven modeling is a viable option. For the analysis, prediction, design and control of such equation- or data-defined processes, reduced-order models capturing the core of the underlying physical phenomena are critically important. The most frequently used model reduction methods include modal projection methods, linear approximate models and neural network-based reduction. Each method has its own success stories but also possesses limitations that prevent its general applicability.

Specifically, projection-based models for nonlinear systems are fundamentally heuristic due to their dependence on the linear modes used. Data-driven linear modeling techniques, such as dynamic mode decomposition (DMD) and its variants, are unable to capture characteristically nonlinear phenomena, such as coexisting isolated steady states. Finally, machine learning approaches tend to provide unnecessarily large models that are not interpretable and do not perform well outside their training range.

In this short course, we discuss recently developed, general model reduction techniques that do not suffer from the above shortcomings and provide accurate, low-dimensional reduced models for complex nonlinear systems. This technique is based on the theory of spectral submanifolds (SSMs) that are mathematically rigorous nonlinear continuations of linear modal subspaces in oscillatory systems. We first cover the necessary theoretical background in a format accessible to practitioners and illustrate the strength of SSM-based model reduction on select examples from solid and fluid mechanics.

We then offer a tutorial on practical SSM-reduction for high-dimensional (finite-element-grade) mechanical models via the use of the open source package SSMTool. Finally, we offer a similar tutorial on extracting SSM-reduced nonlinear models from time-varying numerical and experimental data via the open source package SSMTool.

Prof. George Haller: George Haller is a professor of Mechanical Engineering at ETH Zürich, where he holds the Chair in Nonlinear Dynamics. His prior appointments include tenured faculty positions at Brown, McGill and MIT. He also served as the first director of Morgan Stanley’s fixed income modeling center. Professor Haller is a former Sloan Fellow, Thomas Hughes Young Investigator (ASME) and a School of Engineering Distinguished Professor (McGill), as well as current external member of the Hungarian Academy of Science. He serves as associate editor at the Journal of Applied Mechanics, feature editor at Nonlinear Dynamics and senior editor at the Journal of Nonlinear Science. He is an elected fellow of SIAM, APS and ASME.

Prof. Shobhit Jain: Shobhit Jain is an assistant professor of Applied Mathematics at TU Delft. He obtained his undergraduate degree in Mechanical Engineering from IIT Roorkee, his M. Sc. degrees in Mechanical Engineering and Applied Mathematics from TU Delft, and his doctoral degree from ETH Zurich. Shobhit has had industrial stints at several engineering firms, gathering experience in heavy engineering, precision and microsystems engineering, and numerical simulations.

Dr. Bálint Kaszás: Bálint Kaszás earned his Bachelor’s and Master’s degrees in Physics from Eötvös Loránd University in Budapest, Hungary. He has obtained his Ph.D. from ETH Zurich, where he is currently a postdoctoral fellow in the research group led by George Haller. His research interests include reduced-order modeling and uncertainty quantification applied to fluid mechanical problems.

The regular course fee is $500 and the student fee is $250. Course fee includes lunches, course handout material, and refreshment breaks. Lodging and additional food or materials are not included.

If the course is cancelled for any reason, the Society for Experimental Mechanics’ liability is limited to the return of the course fees.

Attendees are encouraged to bring their own laptops. None will be provided.