Data-Driven Nonlinear Model Reduction for Fluids and Structures

I discuss a recent dynamical-systems-based alternative to neural networks in the data-driven reduced-order modeling of nonlinear phenomena. Specifically, I show that spectral submanifolds (SSMs) provide very low-dimensional attractors in a broad family of physical problems ranging from structural vibrations to transitions in shear flows. A data-driven identification of the reduced dynamics on these SSMs gives a mathematically rigorous way to construct accurate and predictive reduced-order models without the use of governing equations. I illustrate SSM-based reduced modeling on several numerical and experimental data sets from fluid sloshing, hydrogel oscillations, transitions in plane Couette and pipe flows, and model-predictive control of soft robots.