2025/02/07 by Simone Manti, Ping-Hsuan Tsai, Manti, Simone +5 · 2 citations
Computer Science · Engineering · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Hydraulic and Pneumatic Systems #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Modeling and Simulation Systems #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2502.04703
openalex publication_date 2025/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Data-driven closures correct the standard reduced order models (ROMs) to increase their accuracy in under-resolved, convection-dominated flows. There are two types of data-driven ROM closures in current use: (i) structural, with simple ansatzes (e.g., linear or quadratic); and (ii) machine learning-based, with neural network ansatzes. We propose a novel symbolic regression (SR) data-driven ROM closure strategy, which combines the advantages of current approaches and eliminates their drawbacks. As a result, the new data-driven SR closures yield ROMs that are interpretable, parsimonious, accurate, generalizable, and robust. To compare the data-driven SR-ROM closures with the structural and machine learning-based ROM closures, we consider the data-driven variational multiscale ROM framework and two under-resolved, convection-dominated test problems: the flow past a cylinder and the lid-driven cavity flow at Reynolds numbers Re = 10000, 15000, and 20000. This numerical investigation shows that the new data-driven SR-ROM closures yield more accurate and robust ROMs than the structural and machine learning ROM closures.