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

  Jiang Yang, Quanhui Zhu

  2022-02-09

  47124 4540 Pages:42-67

• Convergence Analysis of a Quasi-Monte Carlo-Based Deep Learning Algorithm for Solving Partial Differential Equations

  Fengjiang Fu, Xiaoqun Wang

  2023-08-29

  28404 2513 Pages:668-700

• Sparse Deep Neural Network for Nonlinear Partial Differential Equations

  Yuesheng Xu, Taishan Zeng

  2023-01-13

  34437 3135 Pages:58-78

• A QMC-Deep Learning Method for Diffusivity Estimation in Random Domains

  Liyao Lyu, Zhiwen Zhang, Jingrun Chen

  2020-12-02

  52790 2973 Pages:908-927

• HRW: Hybrid Residual and Weak Form Loss for Solving Elliptic Interface Problems with Neural Network

  Muzhou Hou, Yinghao Chen, Shen Cao, Yuntian Chen, Jinyong Ying

  2023-11-07

  29871 2542 Pages:883-913

• A Stabilized Physics Informed Neural Networks Method for Wave Equations

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

  2024-12-11

  11793 1380 Pages:1100-1127

• Uncertainty Quantification with Physics-Informed Generative Process Distributions for the Linear Diffusion Equation

  Wei Zhang, Hui Xie, Tengchao Yu, Heng Yong

  2025-09-01

  5132 410 Pages:794-816

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

  Jichang Xiao, Xiaoqun Wang

  2024-12-11

  11943 1346 Pages:996-1017