A Discontinuity Capturing Shallow Neural Network for Elliptic Interface
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A Discontinuity Capturing Shallow Neural Network for Elliptic Interface Problems

10 June 2021

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Papers citing "A Discontinuity Capturing Shallow Neural Network for Elliptic Interface Problems"

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Title
A Shallow Ritz Method for Elliptic Problems with Singular Sources M. Lai Che-Chia Chang Wei-Syuan Lin Wei-Fan Hu Te-Sheng Lin 43 14 0 26 Jul 2021
PFNN: A Penalty-Free Neural Network Method for Solving a Class of Second-Order Boundary-Value Problems on Complex Geometries H. Sheng Chao Yang 52 118 0 14 Apr 2020
A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems Lars Ruthotto Stanley Osher Wuchen Li L. Nurbekyan Samy Wu Fung AI4CE 140 220 0 04 Dec 2019
Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs Z. Cai Jingshuang Chen Min Liu Xinyu Liu 60 89 0 05 Nov 2019
Approximating Continuous Functions by ReLU Nets of Minimal Width Boris Hanin Mark Sellke 107 239 0 31 Oct 2017
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 125 1,393 0 30 Sep 2017
The Expressive Power of Neural Networks: A View from the Width Zhou Lu Hongming Pu Feicheng Wang Zhiqiang Hu Liwei Wang 99 899 0 08 Sep 2017
DGM: A deep learning algorithm for solving partial differential equations Justin A. Sirignano K. Spiliopoulos AI4CE 97 2,067 0 24 Aug 2017
Automatic differentiation in machine learning: a survey A. G. Baydin Barak A. Pearlmutter Alexey Radul J. Siskind PINN AI4CE ODL 172 2,820 0 20 Feb 2015
Adam: A Method for Stochastic Optimization Diederik P. Kingma Jimmy Ba ODL 2.1K 150,364 0 22 Dec 2014