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This paper aims at studying the difference between Ritz-Galerkin (R-G) method and deep neural network (DNN) method in solving partial differential equations (PDEs) to better understand deep learning.
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Z. Q. Cai, J. S. Chen, M. Liu and X. Y. Liu, Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs, J. Comput. Phys., 420(2020), 109707
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Z. Q. Liu, W. Cai and Z. Q. J. Xu, Multi-scale deep neural network (mscaleDNN) for solving Poisson-Boltzmann equation in complex domains, Commun. Comput. Phys., to appear
Cited in the paper.
Z. Q. J. Xu, Y. Y. Zhang, T. Luo, Y. Y. Xiao and Z. Ma, Frequency principle: Fourier analysis sheds light on deep neural networks, Commun. Comput. Phys., to appear
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2020
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