Bio:
Before joining USU, I was a postdoctoral scholar in the Department of Mathematics at Purdue University (Fall 2024–2025), and a Van Vleck Visiting Assistant Professor/ Postdoctoral Scholar at the University of Wisconsin–Madison (Fall 2021–2024). I got my Ph.D. in Mathematics from Virginia Tech under the supervision of Prof. Traian Iliescu. I obtained my bachelor’s degree from Sun Yat-sen University (中山大学), in Guangzhou, China.
Title: Stochastic Reduced Order Modeling for Complex Systems
Abstract: Complex systems such as turbulent flows are often too expensive to simulate in full detail, and reduced order models (ROMs) that keep only a few dominant modes offer a much cheaper alternative. For chaotic systems, a good ROM should stay stable over long times, reproduce the statistics of the full model, and help recover unobserved states from partial observations. In this talk, I will present two approaches to building stochastic ROMs. The first learns a stochastic model directly from data, estimating the deterministic and stochastic parts together while building energy conservation into the learning step. The second is a multiscale model that keeps the large-scale dynamics and represents the effect of smaller scales with simple closure terms and random forcing, a structure that allows unobserved states to be estimated with closed-form formulas instead of ensemble methods. Both approaches are applied to complex PDEs such as the stochastic Burgers equation and the quasi-geostrophic equations, where the stochastic ROMs remain stable and capture the key statistics, while standard ROMs can become inaccurate or unstable.