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math.NA2026
Physics-Informed Learning of Probabilistic Gegenbauer Reconstruction for Transport-Dominated Problems
Lei Yan, Yan Jiang
Transport-dominated problems remain challenging for data-driven methods, which often exhibit severe numerical oscillations near shocks or steep gradients due to globally supported…
math.NA2026
Post-Processing Reduced-Order Models for Transport-Dominated Problems by Gegenbauer Reconstruction
Lei Yan, Yan Jiang, Chi-Wang Shu
In this paper, we develop a physics-based post-processing technique for data-driven reduced-order models (ROMs) of transport-dominated problems. Besides the slow decay of the Kolmo…