1 code implementation • 16 Oct 2022 • Yu-Hau Tseng, Te-Sheng Lin, Wei-Fan Hu, Ming-Chih Lai
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 has discontinuous first derivatives on the interface.
no code implementations • 11 Oct 2022 • Wei-Fan Hu, Te-Sheng Lin, Yu-Hau Tseng, Ming-Chih Lai
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 interfaces.
no code implementations • 3 Mar 2022 • Wei-Fan Hu, Yi-Jun Shih, Te-Sheng Lin, Ming-Chih Lai
To track the surface, we additionally introduce a prescribed hidden layer to enforce the topological structure of the surface and use the network to learn the homeomorphism between the surface and the prescribed topology.
no code implementations • 26 Jul 2021 • Ming-Chih Lai, Che-Chia Chang, Wei-Syuan Lin, Wei-Fan Hu, Te-Sheng Lin
We first introduce the energy functional of the problem and then transform the contribution of singular sources to a regular surface integral along the interface.
1 code implementation • 10 Jun 2021 • Wei-Fan Hu, Te-Sheng Lin, Ming-Chih Lai
In this paper, a new Discontinuity Capturing Shallow Neural Network (DCSNN) for approximating $d$-dimensional piecewise continuous functions and for solving elliptic interface problems is developed.