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• Quasi-Monte Carlo Sampling for Solving Partial Differential Equations by Deep Neural Networks

  Jingrun Chen, Rui Du, Panchi Li, Liyao Lyu

  2021-01-26

  46499 2782 Pages:377-404

• A Stabilized Physics Informed Neural Networks Method for Wave Equations

  Yuling Jiao, Yuhui Liu, Jerry Zhijian Yang, Cheng Yuan

  2024-12-11

  11927 1432 Pages:1100-1127

• A Local Deep Learning Method for Solving High Order Partial Differential Equations

  Jiang Yang, Quanhui Zhu

  2022-02-09

  47233 4619 Pages:42-67

• Error Analysis for Empirical Risk Minimization over Clipped ReLU Networks in Solving Linear Kolmogorov Partial Differential Equations

  Jichang Xiao, Xiaoqun Wang

  2024-12-11

  12052 1376 Pages:996-1017

• Sparse Deep Neural Network for Nonlinear Partial Differential Equations

  Yuesheng Xu, Taishan Zeng

  2023-01-13

  34541 3191 Pages:58-78

• MC-Nonlocal-PINNs: Handling Nonlocal Operators in PINNs via Monte Carlo Sampling

  Xiaodong Feng, Yue Qian, Wanfang Shen

  2023-08-29

  28448 2481 Pages:769-791