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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

  52020 3444 Pages:379-411

• MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs

  Lulu Zhang, Tao Luo, Yaoyu Zhang, Weinan E, Zhi-Qin John Xu, Zheng Ma

  2022-08-11

  307216 3644 Pages:299-335

• Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws, Part II: 2D Problems

  Haoxiang Huang, Vigor Yang, Yingjie Liu

  2023-11-08

  77233 3704 Pages:907-933

• An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems

  Liang Yan, Tao Zhou

  2020-11-18

  67468 3473 Pages:2180-2205

• Solving Allen-Cahn and Cahn-Hilliard Equations Using the Adaptive Physics Informed Neural Networks

  Colby L. Wight, Jia Zhao

  2021-01-13

  59563 3989 Pages:930-954

• Scale-Decomposed Physics-Informed Neural Networks for Singular Perturbation Problems

  Lei Zhang, Guowei He

  2026-01-18

  1020 230 Pages:1267-1298

• Generalization Error Analysis of Neural Networks with Gradient Based Regularization

  Lingfeng Li, Xue-Cheng Tai, Jiang Yang

  2022-10-28

  45817 3322 Pages:1007-1038

• Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems

  Sidi Wu, Aiqing Zhu, Yifa Tang, Benzhuo Lu

  2023-03-13

  41082 3304 Pages:596-627

• VPVnet: A Velocity-Pressure-Vorticity Neural Network Method for the Stokes’ Equations under Reduced Regularity

  Yujie Liu, Chao Yang

  2022-03-03

  45626 3272 Pages:739-770

• Multi-Scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains

  Bo Wang, Wenzhong Zhang, Wei Cai

  2020-11-18

  64562 3363 Pages:2139-2157

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

  Huifang Zhou, Zhiqiang Sheng

  2026-01-15

  3200 292 Pages:147-184

• A New Artificial Neural Network Method for Solving Schrödinger Equations on Unbounded Domains

  Joshua P. Wilson, Weizhong Dai, Aniruddha Bora, Jacob C. Boyt

  2022-10-28

  47604 3514 Pages:1039-1060

• Asymptotic-Preserving Neural Networks for Multiscale Kinetic Equations

  Shi Jin, Zheng Ma, Keke Wu

  2024-04-10

  25505 2190 Pages:693-723

• Two-Scale Neural Networks for Partial Differential Equations with Small Parameters

  Qiao Zhuang, Chris Ziyi Yao, Zhongqiang Zhang, George Em Karniadakis

  2025-08-23

  6670 630 Pages:603-629

• Finite Neuron Method and Convergence Analysis

  Jinchao Xu

  2020-11-18

  70593 3842 Pages:1707-1745

• 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

  74180 3751 Pages:1970-2001

• 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

  770 108 Pages:1231-1266

• Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability

  Zhen Gao, Qi Liu, Jan S. Hesthaven, Bao-Shan Wang, Wai Sun Don, Xiao Wen

  2021-04-30

  50092 4592 Pages:97-123

• 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

  35602 2925 Pages:813-836

• DL-PDE: Deep-Learning Based Data-Driven Discovery of Partial Differential Equations from Discrete and Noisy Data

  Hao Xu, Haibin Chang, Dongxiao Zhang

  2021-01-13

  55429 3560 Pages:698-728

• MHDnet: Physics-Preserving Learning for Solving Magnetohydrodynamics Problems

  Xiaofei Guan, Boya Hu, Shipeng Mao, Xintong Wang, Zihao Yang

  2024-10-29

  21791 1258 Pages:943-976

• Hamiltonian Reduction Using a Convolutional Auto-Encoder Coupled to a Hamiltonian Neural Network

  Raphaël Côte, Emmanuel Franck, Laurent Navoret, Guillaume Steimer, Vincent Vigon

  2025-09-02

  11895 916 Pages:315-352

• Neural-Network-Augmented Empirical Interpolation Method for Field Reconstruction with Noise and Vibration Tolerance

  Han Li, Helin Gong, Chuanju Xu

  2026-01-03

  1920 80 Pages:855-883

• Learning Invariant Representation of Multiscale Hyperelastic Constitutive Law from Sparse Experimental Data

  Rui He, Junzhi Cui, Zihao Yang, Jieqiong Zhang, Xiaofei Guan

  2023-09-04

  34253 2836 Pages:392-417

• 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

  374 24 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

  59115 3457 Pages:1020-1048

• Continuous-Variable Deep Quantum Neural Networks for Flexible Learning of Structured Classical Information

  Jasvith Raj Basani, Aranya Bhattacherjee

  2021-08-10

  46296 3032 Pages:1216-1231