演講者：蔡秉軒教授 (國立陽明交通大學應用數學系)

日   期：2026 年 10 月 28 日（星期三）13:30

地   點：國立高雄大學理學院 408 室

講   題：Toward Reliable and Scalable Reduced-Order Models for Turbulent Flows

摘   要：
    Advances in high-performance computing have enabled high-fidelity simulations of complex turbulent flows. Reduced-order modeling (ROM) aims to accelerate these simulations for many-query tasks such as engineering design, control, and parametric studies. However, ROMs for turbulent flows can exhibit instability and degraded predictive accuracy,while applying them to large-scale problems is hindered by high training costs and limited or unavailable training data.
    In this talk, I will present recent progress toward improving the reliability and scalability of ROMs. The first part focuses on stabilization strategies for under-resolved ROMs, in which spatial filters play a central role. However, fundamental questions remain regarding the choice of filter and the determination of its parameters. To address these issues, we develop a data-driven stabilization operator, StabOp, that replaces traditional spatial filters and is trained through PDE-constrained optimization to improve accuracy for a given quantity of interest and stabilization strategy. Numerical results for convection-dominated and turbulent flows demonstrate that ROMs using StabOp outperform those using classical spatial filters in predictive accuracy.
    In the second part of the talk, a bottom-up approach will be presented to construct scalable ROMs through domain decomposition and nonlinear manifold approximations. Local reduced representations are trained using data from smaller configurations and assembled through physics-based coupling to model larger systems. Results for the two-dimensional Burgers equation demonstrate the feasibility of predicting dynamics on larger domains without requiring training data from the full target system.