no code implementations • 31 Jan 2024 • Hwi Lee, Zhen Chao, Harris Cobb, Yingjie Liu, Dexuan Xie
Since the input data of the neural network scheme only involves a small local patch of coarse grid solutions, which the finite element solver can quickly produce, the PNPic deep learning solver can be trained much faster than any corresponding conventional global neural network solvers.
no code implementations • 6 Feb 2023 • Harris Cobb, Hwi Lee, Yingjie Liu
In contrast with existing research work on applying neural networks to directly solve PDEs, our method takes advantage of the local domain of dependence of the Maxwell's equation in the input solution patches, and is therefore simpler, yet still robust.
