Nonlinear Reduced-Order Modeling from Data

I discuss a recent dynamical-systems-based alternative to machine learning in the data-driven reduced-order modeling of nonlinear phenomena. Specifically, spectral submanifolds (SSMs) represent very low-dimensional attractors in a large family of physical problems ranging from wing oscillations to transitions in pipe flows. A data-driven identification of the reduced dynamics on these SSMs gives a rigorous way to construct accurate and predictive reduced-order models for solids, fluids, and controls without the use of governing equations. I illustrate this on problems that include accelerated finite-element simulations of large structures, prediction of transitions in pipe flows, reduced-order modeling of fluid sloshing in a tank, and model-predictive control of soft robots.