Learning Reduced-Complexity Models for Nonlinear Dynamical Systems from Data

Nonlinear dynamical systems are ubiquitous in science and engineering. While high-fidelity models based on first principle has been well established, reduced-complexity models are of particular interest in recent years due to its feasibility for many-query tasks, e.g., uncertainty propagation, optimal control and design. In this talk, I will discuss two recent works from my group at RPI in this theme. For the first half, I will talk about learning reduced complexity models in the light of learning Koopman operator for control. We highlight our solutions to address several issues when standard algorithm is applied, e.g., noisy data, instability, efficient curation of training data, choice of observables. We demonstrate the benefits of our proposed framework on model predictive control of a Koopman-based surrogate model for CartPole problem. For the second half, I will talk about learning reduced complexity models in the light of surrogate model of time-dependent partial differential equations from data. In contrast to existing frameworks, our model ensures stability of learned surrogate model through a stable parametrization of Koopman operator and trapping theorem of linear quadratic dynamics. Moreover, our model is agnostic to mesh, scalable to 3D problems and could only require a few sensor measurement during inference stage. We demonstrate the benefits of our model over several state-of-the-art neural operator frameworks on 2D wave propagation, 2D Navier-Stokes in a periodic box, shallow water equations.

Shaowu Pan is currently a tenure-track assistant professor in the Department of Mechanical, Aerospace, and Nuclear Engineering at RPI starting from 2022 Fall. He is also affiliated with the Rensselaer-IBM Artificial Intelligence Research Collaboration (AIRC). He received MS and PhD in Aerospace Engineering and Scientific Computing from the University of Michigan, Ann Arbor in April 2021. Then he started as a Postdoctoral Scholar in the AI Institute in Dynamic Systems at the University of Washington, Seattle from 2021 to 2022. His research interests are scientific machine learning for large-scale PDE systems and operator-theoretic modeling and control of nonlinear systems.