<p>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 of physical importance. 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, shear flows, plant dynamics, and the model-predictive control of soft robots.</p>
