Search Results

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

  Bo Li, Shanshan Tang, Haijun Yu

  2019-12-07

  52007 3443 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

  26429 2324 Pages:467-497

• A New Function Space from Barron Class and Application to Neural Network Approximation

  Yan Meng, Pingbing Ming

  2023-01-24

  38974 3535 Pages:1361-1400

• 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

  4554 375 Pages:1453-1497

• High Order Deep Neural Network for Solving High Frequency Partial Differential Equations

  Zhipeng Chang, Ke Li, Xiufen Zou, Xueshuang Xiang

  2022-01-27

  46266 3535 Pages:370-397

• Deep Network Approximation Characterized by Number of Neurons

  Zuowei Shen, Haizhao Yang, Shijun Zhang

  2020-11-18

  69179 3702 Pages:1768-1811

• Butterfly-Net: Optimal Function Representation Based on Convolutional Neural Networks

  Yingzhou Li, Xiuyuan Cheng, Jianfeng Lu

  2020-11-18

  63880 3510 Pages:1838-1885

• 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

  52172 3171 Pages:1272-1295

• 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

  28537 2079 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

  36490 2925 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

  59545 3983 Pages:930-954

• Generalization Error Analysis of Neural Networks with Gradient Based Regularization

  Lingfeng Li, Xue-Cheng Tai, Jiang Yang

  2022-10-28

  45808 3320 Pages:1007-1038

• Ensemble Gradient for Learning Turbulence Models from Indirect Observations

  Carlos A. Michelén Ströfer, Xin-Lei Zhang, Heng Xiao

  2021-10-26

  80762 3742 Pages:1269-1289

• Finite Neuron Method and Convergence Analysis

  Jinchao Xu

  2020-11-18

  70584 3841 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

  64547 3360 Pages:2139-2157

• Improved Randomized Neural Network Methods with Boundary Processing for Solving Elliptic Equations

  Huifang Zhou, Zhiqiang Sheng

  2026-01-15

  3177 283 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

  74155 3747 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

  35599 2924 Pages:813-836

• Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank

  Tao Tang, Jiang Yang, Yuxiang Zhao, Quanhui Zhu

  2026-03-16

  277 11 Pages:61-87

• Convergence Rate Analysis for Deep Ritz Method

  Chenguang Duan, Yuling Jiao, Yanming Lai, Dingwei Li, Xiliang Lu, Jerry Zhijian Yang

  2022-03-30

  59109 3453 Pages:1020-1048

• Convergence Analysis for Over-Parameterized Deep Learning

  Yuling Jiao, Xiliang Lu, Peiying Wu, Jerry Zhijian Yang

  2024-07-29

  28080 2172 Pages:71-103

• A Complete Error Analysis of PINNs for Elliptic Equations Using Projected Stochastic Gradient Descent

  Yuling Jiao, Ruoxuan Li, Defeng Sun, Peiying Wu, Jerry Zhijian Yang

  2026-04-10

  17 5 Pages:27-60

• Nonlinear Reduced DNN Models for State Estimation

  Wolfgang Dahmen, Min Wang, Zhu Wang

  2022-07-06

  42933 3767 Pages:1-40

• Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions

  Yulei Liao, Pingbing Ming

  2021-03-24

  53487 3558 Pages:1365-1384

• A Causality-DeepONet for Causal Responses of Linear Dynamical Systems

  Lizuo Liu, Kamaljyoti Nath, Wei Cai

  2024-06-14

  36416 1891 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

  9320 578 Pages:942-974