2024/08/09 by Soraya Terrab, Samy Wu Fung, Terrab, Soraya +3
Computer Science · Earth and Planetary Sciences · Physics and Astronomy · #65M99 #FOS: Mathematics #Image and Signal Denoising Methods #Meteorological Phenomena and Simulations #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2408.05193
openalex publication_date 2024/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We present a hybrid filter that is only applied to the approximation at the final time and allows for reducing errors away from a shock as well as near a shock. It is designed for discontinuous Galerkin approximations to PDEs and combines a rigorous moment-based Smoothness-Increasing Accuracy-Conserving (SIAC) filter with a data-driven CNN filter. While SIAC improves accuracy in smooth regions, it fails to reduce the O(1) errors near discontinuities, particularly in inviscid compressible flows with shocks. Our hybrid SIAC-CNN filter, trained exclusively on top-hat functions, enforces consistency constraints globally and higher-order moment conditions in smooth regions, reducing both ℓ2 and ℓ_∞ errors near discontinuities and preserving theoretical accuracy in smooth regions. We demonstrate its effectiveness on the Euler equations for the Lax, Sod, and Shu-Osher shock-tube problems.