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  • Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units

    Bo Li, Shanshan Tang, Haijun Yu
    2019-12-07
    51826 3403 Pages:379-411
  • A Conservative and Positivity-Preserving Method for Solving Anisotropic Diffusion Equations with Deep Learning

    Hui Xie, Li Liu, Chuanlei Zhai, Xuejun Xu, Heng Yong
    2024-03-13
    26287 2282 Pages:467-497
  • Adaptive Basis-Inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features

    Ke Li, Yaqin Zhang, Yunqing Huang, Chenyue Xie, Xueshuang Xiang
    2025-09-18
    4374 321 Pages:1453-1497
  • A New Function Space from Barron Class and Application to Neural Network Approximation

    Yan Meng, Pingbing Ming
    2023-01-24
    38800 3489 Pages:1361-1400
  • High Order Deep Neural Network for Solving High Frequency Partial Differential Equations

    Zhipeng Chang, Ke Li, Xiufen Zou, Xueshuang Xiang
    2022-01-27
    46148 3482 Pages:370-397
  • Deep Network Approximation Characterized by Number of Neurons

    Zuowei Shen, Haizhao Yang, Shijun Zhang
    2020-11-18
    68957 3646 Pages:1768-1811
  • A Rate of Convergence of Physics Informed Neural Networks for the Linear Second Order Elliptic PDEs

    Yuling Jiao, Yanming Lai, Dingwei Li, Xiliang Lu, Fengru Wang, Yang Wang, Jerry Zhijian Yang
    2022-03-30
    51988 3131 Pages:1272-1295
  • Butterfly-Net: Optimal Function Representation Based on Convolutional Neural Networks

    Yingzhou Li, Xiuyuan Cheng, Jianfeng Lu
    2020-11-18
    63722 3467 Pages:1838-1885
  • A Data-Driven Scale-Invariant Weighted Compact Nonlinear Scheme for Hyperbolic Conservation Laws

    Zixuan Zhang, Yidao Dong, Yuanyang Zou, Hao Zhang, Xiaogang Deng
    2024-05-06
    28423 2043 Pages:1120-1154
  • An Efficient Neural-Network and Finite-Difference Hybrid Method for Elliptic Interface Problems with Applications

    Wei-Fan Hu, Te-Sheng Lin, Yu-Hau Tseng, Ming-Chih Lai
    2023-05-12
    36361 2889 Pages:1090-1105
  • Solving Allen-Cahn and Cahn-Hilliard Equations Using the Adaptive Physics Informed Neural Networks

    Colby L. Wight, Jia Zhao
    2021-01-13
    59168 3906 Pages:930-954
  • Generalization Error Analysis of Neural Networks with Gradient Based Regularization

    Lingfeng Li, Xue-Cheng Tai, Jiang Yang
    2022-10-28
    45663 3276 Pages:1007-1038
  • Ensemble Gradient for Learning Turbulence Models from Indirect Observations

    Carlos A. Michelén Ströfer, Xin-Lei Zhang, Heng Xiao
    2021-10-26
    80671 3711 Pages:1269-1289
  • Finite Neuron Method and Convergence Analysis

    Jinchao Xu
    2020-11-18
    70404 3799 Pages:1707-1745
  • Multi-Scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains

    Bo Wang, Wenzhong Zhang, Wei Cai
    2020-11-18
    64332 3316 Pages:2139-2157
  • Improved Randomized Neural Network Methods with Boundary Processing for Solving Elliptic Equations

    Huifang Zhou, Zhiqiang Sheng
    2026-01-15
    2930 185 Pages:147-184
  • Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains

    Ziqi Liu, Wei Cai, Zhi-Qin John Xu
    2020-11-18
    73856 3682 Pages:1970-2001
  • A Rate of Convergence of Weak Adversarial Neural Networks for the Second Order Parabolic PDEs

    Yuling Jiao, Jerry Zhijian Yang, Cheng Yuan, Junyu Zhou
    2023-10-07
    35482 2884 Pages:813-836
  • Convergence Rate Analysis for Deep Ritz Method

    Chenguang Duan, Yuling Jiao, Yanming Lai, Dingwei Li, Xiliang Lu, Jerry Zhijian Yang
    2022-03-30
    58970 3389 Pages:1020-1048
  • Convergence Analysis for Over-Parameterized Deep Learning

    Yuling Jiao, Xiliang Lu, Peiying Wu, Jerry Zhijian Yang
    2024-07-29
    27948 2069 Pages:71-103
  • Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions

    Yulei Liao, Pingbing Ming
    2021-03-24
    53300 3485 Pages:1365-1384
  • Nonlinear Reduced DNN Models for State Estimation

    Wolfgang Dahmen, Min Wang, Zhu Wang
    2022-07-06
    42845 3718 Pages:1-40
  • A Causality-DeepONet for Causal Responses of Linear Dynamical Systems

    Lizuo Liu, Kamaljyoti Nath, Wei Cai
    2024-06-14
    36253 1846 Pages:1194-1228
  • 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
1 - 24 of 24 items
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