Published: Jul 15, 2025 by Daning Huang
We are happy to announce the award of an NSF project from the Computational and Data-Enabled Science and Engineering (CDS&E) program, titled Leveraging Geometric Structure in Learning Dynamical Systems. The project is joint with Prof. John Harlim from Penn State Math.
The goal of the project is to reveal geometric structures encoded in the measured time series of the dynamics, i.e., the data manifold, to enable compact reduced-order modeling for scalable numerical simulations. Specifically, we will consider (1) learning dynamics on manifolds with provable preservation of geometrical constraints; (2) learning Lie symmetry groups of dynamics, that leads to scaling/similarity laws of complex dynamical systems.
The first aim generalizes our physics-infused reduced-order modeling (ROM) methodology from the NSF CAREER project into a geometry-infused ROM. The second aim is a leap from our prior work on aerothermoelastic scaling (brutal force in engineering) to a more systematic and elegant mathematical treatment via Lie group theory.