Using Gradient Data to Preserve what Matters in Reduced-Order Models of Dynamical Systems
Reduced-order models (ROMs) seek low-dimensional descriptions of complex dynamical systems to enable fast simulation, forecasting, and control. Most modern ROMs for highly nonlinear, large-scale systems such as those arising in fluid dynamics choose reduced modeling variables according to how well they reconstruct observed system states. This principle is highly effective when trajectories lie near a low-dimensional manifold, but it can fail dramatically when small, low-variance perturbations have a large effect on future behavior. I will present an alternative viewpoint in which reduced state variables are chosen to preserve the quantities that matter for a specific prediction or control task. The key additional information comes from gradients, which reveal directions in state space that strongly influence future outputs, rare events, or control objectives. I will introduce sensitivity-balanced model reduction and illustrate it through nonlinear fluid-flow forecasting, prediction and suppression of extreme events, and recent work on reduced-order optimal control. These examples suggest a broader framework for constructing ROMs that preserve sensitivity rather than state reconstruction alone.
Bio: Samuel Otto joined the Sibley School of Mechanical and Aerospace Engineering faculty as an assistant professor in July 2024. His lab exploits mathematical structure and data to develop faster algorithms for simulating, learning, reducing, and controlling complex engineering systems. Prior to this, he was a Postdoctoral Scholar at the AI Institute in Dynamic Systems at the University of Washington. He received his Ph.D. in mechanical and aerospace engineering from Princeton University in May 2022 and his B.S. in aeronautics and astronautics from Purdue University in 2016. He enjoys science fiction, fantasy, and weightlifting and can usually be found in a coffee shop with a math textbook.