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 mathematical modeling center. Professor Haller is a former Sloan Fellow, Thomas Hughes Young Investigator (ASME) and School of Engineering Distinguished Professor (McGill), as well as a 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, and the recipient of the 2023 Stanley Corrsin Award of the American Physical Society.
Abstract
I discuss a dynamical systems alternative to neural networks in the data-driven reduced-order modeling of nonlinear phenomena. Specifically, the recent concept of spectral submanifolds (SSMs) provides very low-dimensional attractors in virtually all dynamics problems. A data-driven identification of the reduced dynamics on these SSMs gives a mathematically justified way to construct accurate and predictive reduced-order models for solids, fluids and controls without the use of governing equations. I illustrate this on physical problems including structural vibrations, fluid-structure interactions, hydrogel oscillations, plant dynamics and the model-predictive control of soft robots.
