Welcome to my homepage! I am an Assistant Professor in the Department of Applied Mathematics at National Yang Ming Chiao Tung University (NYCU). Before joining NYCU, I was a postdoctoral associate in the Department of Mathematics at Virginia Tech, working with Prof. Traian Iliescu. I earned my Ph.D. in Computer Science from the University of Illinois at Urbana-Champaign in 2023, where I was advised by Prof. Paul Fischer.
My research focuses on the development of data-driven reduced-order models for complex multiscale systems, with applications to fluid and plasma dynamics. In particular, my work encompasses model development—constructing accurate and efficient data-driven ROMs; numerical analysis—establishing fundamental mathematical properties such as stability, consistency, convergence, and parameter scalings; and numerical simulation—evaluating new data-driven ROMs on challenging problems in science and engineering.
This project focused on developing error-indicated parametric reduced-order models for unsteady natural convection. The approach combines POD-hGreedy sampling with stabilized ROMs to efficiently predict flow and heat-transfer quantities in challenging regimes involving bifurcations, multiple solutions, and spatio-temporal chaos.
“Parametric Model-Order-Reduction Development for Unsteady Convection”
by P.-H. Tsai and P. Fischer