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Multi-scale DNN

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多尺度神经网络解微分方程 文献[9,12]

[24] (Alphabetic order) Xi-An Li, Zhi-Qin John Xu, Lei Zhang*, Subspace Decomposition based DNN algorithm for elliptic type multi-scale PDEs. arxiv 2112.06660 (2021) pdf, and in arxiv.

[12] (Alphabetic order) Xi-An Li, Zhi-Qin John Xu* , Lei Zhang, A multi-scale DNN algorithm for nonlinear elliptic equations with multiple scales, arxiv 2009.14597, (2020) Communications in Computational Physics (CiCP). pdf, and in web, and in arxiv, some code is in github.

Note: [9] is a comprehensive version of [8]

[9] Ziqi Liu, Wei Cai, Zhi-Qin John Xu* , Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains, arxiv 2007.11207 (2020) Communications in Computational Physics (CiCP). pdf, and in web, some code is in github.

[8] (Alphabetic order) Wei Cai, Zhi-Qin John Xu* , Multi-scale Deep Neural Networks for Solving High Dimensional PDEs, arxiv 1910.11710 (2019) pdf, and in arxiv