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math.NA2025
Data-driven optimized high-order WENO schemes with low-dissipation and low-dispersion
Jinrui Zhou, Yiqi Gu, Song Jiang +3
Classical high-order weighted essentially non-oscillatory (WENO) schemes are designed to achieve optimal convergence order for smooth solutions and to maintain non-oscillatory beha…
math.NA2025
Learning high-accuracy numerical schemes for hyperbolic equations on coarse meshes
Jinrui Zhou, Yiqi Gu, Hua Shen +3
When solving partial differential equations using classical schemes such as finite difference or finite volume methods, sufficiently fine meshes and carefully designed schemes are…
math.NA2024
Macroscopic auxiliary asymptotic preserving neural networks for the linear radiative transfer equations
Hongyan Li, Song Jiang, Wenjun Sun +2
We develop a Macroscopic Auxiliary Asymptotic-Preserving Neural Network (MA-APNN) method to solve the time-dependent linear radiative transfer equations (LRTEs), which have a multi…