Search Results

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

  Jingrun Chen, Rui Du, Panchi Li, Liyao Lyu

  2021-01-26

  DOI:10.4208/nmtma.OA-2020-0062

  46504 2785 pp. 377-404

• A Stabilized Physics Informed Neural Networks Method for Wave Equations

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

  2024-12-11

  DOI:10.4208/nmtma.OA-2024-0044

  11931 1439 pp. 1100-1127

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

  Jiang Yang, Quanhui Zhu

  2022-02-09

  DOI:10.4208/nmtma.OA-2021-0035

  47238 4622 pp. 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

  DOI:10.4208/nmtma.OA-2024-0026

  12055 1377 pp. 996-1017

• Sparse Deep Neural Network for Nonlinear Partial Differential Equations

  Yuesheng Xu, Taishan Zeng

  2023-01-13

  DOI:10.4208/nmtma.OA-2022-0104

  34550 3197 pp. 58-78

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

  Xiaodong Feng, Yue Qian, Wanfang Shen

  2023-08-29

  DOI:10.4208/nmtma.OA-2022-0201

  28455 2484 pp. 769-791