Search Results

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

  Jasvith Raj Basani, Aranya Bhattacherjee

  2021-08-10

  https://doi.org/10.4208/cicp.OA-2020-0173

  46112 2967 pp. 1216-1231

• Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks

  Zhi-Qin John Xu, Yaoyu Zhang, Tao Luo, Yanyang Xiao, Zheng Ma

  2020-11-18

  https://doi.org/10.4208/cicp.OA-2020-0085

  85482 4069 pp. 1746-1767

• Generalization Error in the Deep Ritz Method with Smooth Activation Functions

  Janne Siipola

  2024-04-10

  https://doi.org/10.4208/cicp.OA-2023-0253

  24120 2222 pp. 761-815 Open Access

• Learning Specialized Activation Functions for Physics-Informed Neural Networks

  Honghui Wang, Lu Lu, Shiji Song, Gao Huang

  2023-11-08

  https://doi.org/10.4208/cicp.OA-2023-0058

  34363 2783 pp. 869-906

• Time Integration Schemes Based on Neural Networks for Solving Partial Differential Equations on Coarse Grids

  Xinxin Yan, Zhideng Zhou, Xiaohan Cheng, Xiaolei Yang

  2024-12-02

  https://doi.org/10.4208/cicp.OA-2023-0266

  201 54 pp. 1262-1306

• 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

  https://doi.org/10.4208/cicp.OA-2023-0063

  35332 2836 pp. 813-836

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

  Zhipeng Chang, Ke Li, Xiufen Zou, Xueshuang Xiang

  2022-01-27

  https://doi.org/10.4208/cicp.OA-2021-0092

  46031 3436 pp. 370-397

• Convergence Rate Analysis for Deep Ritz Method

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

  2022-03-30

  https://doi.org/10.4208/cicp.OA-2021-0195

  58803 3318 pp. 1020-1048

• Convergence Analysis for Over-Parameterized Deep Learning

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

  2024-07-29

  https://doi.org/10.4208/cicp.OA-2023-0264

  157 147 pp. 71-103

• 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

  https://doi.org/10.4208/cicp.OA-2018-0035

  66513 6097 pp. 625-650 Open Access

• 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

  https://doi.org/10.4208/cicp.OA-2022-0284

  36233 2866 pp. 1090-1105

• A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions

  Yaqin Zhang, Ke Li, Zhipeng Chang, Xuejiao Liu, Yunqing Huang, Xueshuang Xiang

  2025-07-11

  https://doi.org/10.4208/cicp.OA-2024-0095

  5046 565 pp. 181-222

• 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

  https://doi.org/10.4208/cicp.OA-2023-0162

  28295 2001 pp. 1120-1154

• 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

  https://doi.org/10.4208/cicp.OA-2023-0075

  31686 2665 pp. 1133-1176

• Nonlinear Reduced DNN Models for State Estimation

  Wolfgang Dahmen, Min Wang, Zhu Wang

  2022-07-06

  https://doi.org/10.4208/cicp.OA-2021-0217

  42748 3674 pp. 1-40

• Splitting Physics-Informed Neural Networks for Inferring the Dynamics of Integer- and Fractional-Order Neuron Models

  Simin Shekarpaz, Fanhai Zeng, George Karniadakis

  2024-01-31

  https://doi.org/10.4208/cicp.OA-2023-0121

  29624 2647 pp. 1-37

• Investigating and Mitigating Failure Modes in Physics-Informed Neural Networks (PINNs)

  Shamsulhaq Basir

  2023-06-06

  https://doi.org/10.4208/cicp.OA-2022-0239

  41484 2933 pp. 1240-1269

• 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

  https://doi.org/10.4208/cicp.OA-2020-0241

  47973 3088 pp. 820-850

• Model Reduction with Memory and the Machine Learning of Dynamical Systems

  Chao Ma, Jianchun Wang & Weinan E

  2018-12-08

  https://doi.org/10.4208/cicp.OA-2018-0269

  59155 5193 pp. 947-962 Open Access

• Deep Network Approximation Characterized by Number of Neurons

  Zuowei Shen, Haizhao Yang, Shijun Zhang

  2020-11-18

  https://doi.org/10.4208/cicp.OA-2020-0149

  68719 3581 pp. 1768-1811

• Finite Neuron Method and Convergence Analysis

  Jinchao Xu

  2020-11-18

  https://doi.org/10.4208/cicp.OA-2020-0191

  70207 3742 pp. 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

  https://doi.org/10.4208/cicp.OA-2020-0179

  73632 3621 pp. 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

  https://doi.org/10.4208/cicp.OA-2020-0142

  54997 3468 pp. 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

  https://doi.org/10.4208/cicp.OA-2020-0064

  49858 4428 pp. 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

  https://doi.org/10.4208/cicp.OA-2023-0300

  188 68 pp. 315-352

• MHDnet: Physics-Preserving Learning for Solving Magnetohydrodynamics Problems

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

  2024-10-29

  https://doi.org/10.4208/cicp.OA-2024-0002

  147 68 pp. 943-976

• Deep Unfitted Nitsche Method for Elliptic Interface Problems

  Hailong Guo, Xu Yang

  2022-03-30

  https://doi.org/10.4208/cicp.OA-2021-0201

  52499 3243 pp. 1162-1179