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• Deep Network Approximation Characterized by Number of Neurons

  Zuowei Shen, Haizhao Yang, Shijun Zhang

  2020-11-18

  68957 3646 Pages:1768-1811

• Bi-Orthogonal fPINN: A Physics-Informed Neural Network Method for Solving Time-Dependent Stochastic Fractional PDEs

  Lei Ma, Rongxin Li, Fanhai Zeng, Ling Guo, George Em Karniadakis

  2023-11-08

  31843 2797 Pages:1133-1176

• Nonlinear Reduced DNN Models for State Estimation

  Wolfgang Dahmen, Min Wang, Zhu Wang

  2022-07-06

  42845 3718 Pages:1-40

• Solving Multi-Group Neutron Diffusion Eigenvalue Problem with Decoupling Residual Loss Function

  Shupei Yu, Qiaolin He, Shiquan Zhang, Qihong Yang, Yu Yang, Helin Gong

  2026-01-18

  227 42 Pages:1231-1266

• A Multi-Scale DNN Algorithm for Nonlinear Elliptic Equations with Multiple Scales

  Xi-An Li, Zhi-Qin John Xu, Lei Zhang

  2020-11-18

  67253 3664 Pages:1886-1906

• Numerical Solution of the Incompressible Navier-Stokes Equation by a Deep Branching Algorithm

  Jiang Yu Nguwi, Guillaume Penent, Nicolas Privault

  2023-09-04

  33490 2855 Pages:261-289

• Dirichlet-Neumann Learning Algorithm for Solving Elliptic Interface Problems

  Qi Sun, Xuejun Xu, Haotian Yi

  2025-07-11

  5279 579 Pages:248-284

• Weak Minimization-Sampling Network for Solving PDEs

  Zhenqian E, Weiguo Gao

  2026-01-03

  1690 76 Pages:696-712

• Preface

  2020-11-18

  245 60 Pages:i-i

• Integral Regularization PINNs for Evolution Equations

  Xiaodong Feng, Haojiong Shangguan, Tao Tang, Xiaoliang Wan

  2026-02-15

  3808 139 Pages:356-386

• Data Generation-Based Operator Learning for Solving Partial Differential Equations on Unbounded Domains

  Jihong Wang, Xin Wang, Jing Li, Bin Liu

  2025-05-29

  8885 481 Pages:1383-1416

• Convergence Analysis of PINNs with Over-Parameterization

  Mo Chen, Zhao Ding, Yuling Jiao, Xiliang Lu, Peiying Wu, Jerry Zhijian Yang

  2025-04-27

  9192 531 Pages:942-974