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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

  51684 3375 Pages:379-411

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

  Liang Yan, Tao Zhou

  2020-11-18

  67125 3405 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

  58901 3820 Pages:930-954

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

  Haoxiang Huang, Vigor Yang, Yingjie Liu

  2023-11-08

  76945 3630 Pages:907-933

• Generalization Error Analysis of Neural Networks with Gradient Based Regularization

  Lingfeng Li, Xue-Cheng Tai, Jiang Yang

  2022-10-28

  45537 3242 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

  40769 3224 Pages:596-627

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

  Bo Wang, Wenzhong Zhang, Wei Cai

  2020-11-18

  64184 3294 Pages:2139-2157

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

  Yujie Liu, Chao Yang

  2022-03-03

  45431 3205 Pages:739-770

• 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

  47343 3461 Pages:1039-1060

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

  Huifang Zhou, Zhiqiang Sheng

  2025-11-07

  2596 119 Pages:147-184

• Asymptotic-Preserving Neural Networks for Multiscale Kinetic Equations

  Shi Jin, Zheng Ma, Keke Wu

  2024-04-10

  25172 2100 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

  6003 511 Pages:603-629

• Finite Neuron Method and Convergence Analysis

  Jinchao Xu

  2020-11-18

  70207 3742 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

  73632 3621 Pages:1970-2001

• 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

  54997 3468 Pages:698-728

• 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

  49858 4428 Pages:97-123

• 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

  188 68 Pages:315-352

• MHDnet: Physics-Preserving Learning for Solving Magnetohydrodynamics Problems

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

  2024-10-29

  147 68 Pages:943-976

• 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

  35332 2836 Pages:813-836

• 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

  34022 2764 Pages:392-417

• Convergence Rate Analysis for Deep Ritz Method

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

  2022-03-30

  58803 3318 Pages:1020-1048

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

  Jasvith Raj Basani, Aranya Bhattacherjee

  2021-08-10

  46112 2967 Pages:1216-1231

• An Understanding of the Physical Solutions and the Blow-up Phenomenon for Nonlinear Noisy Leaky Integrate and Fire Neuronal Models

  María J. Cáceres, Alejandro Ramos-Lora

  2021-07-01

  47973 3088 Pages:820-850

• Machine Learning and Computational Mathematics

  Weinan E

  2020-11-18

  88485 4276 Pages:1639-1670

• A Data-Driven Reconstruction for Unstructured Finite Volume Method on Multi-Dimensional Compressible Flows

  Jayeon Joo, Dongseok Kim, Hojun You, Chongam Kim

  2024-12-02

  200 48 Pages:1307-1338

• AutoAMG($θ$): An Auto-Tuned AMG Method Based on Deep Learning for Strong Threshold

  Haifeng Zou, Xiaowen Xu, Chen-Song Zhang, Zeyao Mo

  2024-07-29

  155 138 Pages:200-220

• Data-Driven, Physics-Based Feature Extraction from Fluid Flow Fields Using Convolutional Neural Networks

  Carlos Michelén Ströfer, Jin-Long Wu, Heng Xiao & Eric Paterson

  2018-11-09

  66513 6097 Pages:625-650 Open-access