3 papers
math.NA2026
A Unified Weighted-Loss Physics-Informed Neural Network for Boundary Layer Problems in Singularly Perturbed PDEs
Wei-Fan Hu, Shi-Xiang Zhong, Po-Wen Hsieh +2
Singularly perturbed partial differential equations arise in many applications, including magnetohydrodynamic duct flows, chemical reaction transport systems, and Poisson Boltzmann…
math.NA2025
A categorical embedding discontinuity-capturing shallow neural network for anisotropic elliptic interface problems
Wei-Fan Hu, Te-Sheng Lin, Yu-Hau Tseng +1
In this paper, we propose a categorical embedding discontinuity-capturing shallow neural network for anisotropic elliptic interface problems. The architecture comprises three hidde…
math.NA2023
A hybrid neural-network and MAC scheme for Stokes interface problems
Che-Chia Chang, Chen-Yang Dai, Wei-Fan Hu +2
In this paper, we present a hybrid neural-network and MAC (Marker-And-Cell) scheme for solving Stokes equations with singular forces on an embedded interface in regular domains. As…