Neural network for PDE

科普

Papers

* indicates the corresponding author

#: Equal contribution

[34] Yifan Peng, Dan Hu*, Zhi-Qin John Xu, A Non-Gradient Method for Solving Elliptic Partial Differential Equations with Deep Neural Networks. Journal of Computational Physics (Accepted). in SSRN.

[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.

[20] Lulu Zhang, Tao Luo, Yaoyu Zhang, Weinan E, Zhi-Qin John Xu*, Zheng Ma*, MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs. Communications in Computational Physics (CiCP) (2022) to appear, arxiv 2107.03673 (2021) pdf, and in arxiv.

[15] (Alphabetic order) Jihong Wang, Zhi-Qin John Xu*, Jiwei Zhang*, Yaoyu Zhang, Implicit bias in understanding deep learning for solving PDEs beyond Ritz-Galerkin method, CSIAM Trans. Appl. Math. web, arxiv 2002.07989 (2020). 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

[4] Zhi-Qin John Xu* , Yaoyu Zhang, Tao Luo, Yanyang Xiao, Zheng Ma, Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks, arXiv preprint: 1901.06523, Communications in Computational Physics (CiCP). pdf, and in web, some code is in github (2021世界人工智能大会青年优秀论文提名奖).