78 citations · 381 across the 20 of their papers we have counts for
8 papers · 1 filter
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…
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…
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…
A cusp-capturing PINN for elliptic interface problems
Yu-Hau Tseng, Te-Sheng Lin, Wei-Fan Hu +1
In this paper, we propose a cusp-capturing physics-informed neural network (PINN) to solve discontinuous-coefficient elliptic interface problems whose solution is continuous but ha…
An efficient neural-network and finite-difference hybrid method for elliptic interface problems with applications
Wei-Fan Hu, Te-Sheng Lin, Yu-Hau Tseng +1
A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular…
A shallow physics-informed neural network for solving partial differential equations on surfaces
Wei-Fan Hu, Yi-Jun Shih, Te-Sheng Lin +1
In this paper, we introduce a shallow (one-hidden-layer) physics-informed neural network for solving partial differential equations on static and evolving surfaces. For the static…
A Shallow Ritz Method for Elliptic Problems with Singular Sources
Ming-Chih Lai, Che-Chia Chang, Wei-Syuan Lin +2
In this paper, a shallow Ritz-type neural network for solving elliptic equations with delta function singular sources on an interface is developed. There are three novel features i…
A Discontinuity Capturing Shallow Neural Network for Elliptic Interface Problems
Wei-Fan Hu, Te-Sheng Lin, Ming-Chih Lai
In this paper, a new Discontinuity Capturing Shallow Neural Network (DCSNN) for approximating -dimensional piecewise continuous functions and for solving elliptic interface prob…