A Shallow Ritz Method for Elliptic Problems with Singular Sources

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A Shallow Ritz Method for Elliptic Problems with Singular Sources

26 July 2021

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Papers citing "A Shallow Ritz Method for Elliptic Problems with Singular Sources"

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Title
A Discontinuity Capturing Shallow Neural Network for Elliptic Interface Problems Wei-Fan Hu Te-Sheng Lin M. Lai 117 57 0 10 Jun 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 56 118 0 14 Apr 2020
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
On Empirical Comparisons of Optimizers for Deep Learning Dami Choi Christopher J. Shallue Zachary Nado Jaehoon Lee Chris J. Maddison George E. Dahl 107 259 0 11 Oct 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
Adam: A Method for Stochastic Optimization Diederik P. Kingma Jimmy Ba ODL 2.1K 150,364 0 22 Dec 2014