Search Results

• 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

  DOI:10.4208/cicp.OA-2023-0180

  26439 2329 pp. 467-497

• A Deep Learning Modeling Framework to Capture Mixing Patterns in Reactive-Transport Systems

  N. V. Jagtap, M. K. Mudunuru, K. B. Nakshatrala

  2021-12-06

  DOI:10.4208/cicp.OA-2021-0088

  49510 4115 pp. 188-223

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

  Jasvith Raj Basani, Aranya Bhattacherjee

  2021-08-10

  DOI:10.4208/cicp.OA-2020-0173

  46297 3033 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

  DOI:10.4208/cicp.OA-2020-0085

  86804 4378 pp. 1746-1767

• 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

  DOI:10.4208/cicp.OA-2023-0063

  35606 2926 pp. 813-836

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

  Janne Siipola

  2024-04-10

  DOI:10.4208/cicp.OA-2023-0253

  24367 2450 pp. 761-815 Open Access

• Towards the Efficient Calculation of Quantity of Interest from Steady Euler Equations II: A CNNs-Based Automatic Implementation

  Jingfeng Wang, Guanghui Hu

  2026-01-03

  DOI:10.4208/cicp.OA-2023-0236

  1934 83 pp. 884-918

• 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

  DOI:10.4208/cicp.OA-2023-0266

  15998 1216 pp. 1262-1306

• Learning Specialized Activation Functions for Physics-Informed Neural Networks

  Honghui Wang, Lu Lu, Shiji Song, Gao Huang

  2023-11-08

  DOI:10.4208/cicp.OA-2023-0058

  34829 2964 pp. 869-906

• 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

  DOI:10.4208/cicp.OA-2025-0185

  416 35 pp. 61-87

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

  Zhipeng Chang, Ke Li, Xiufen Zou, Xueshuang Xiang

  2022-01-27

  DOI:10.4208/cicp.OA-2021-0092

  46274 3540 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

  DOI:10.4208/cicp.OA-2021-0195

  59117 3462 pp. 1020-1048

• Convergence Analysis for Over-Parameterized Deep Learning

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

  2024-07-29

  DOI:10.4208/cicp.OA-2023-0264

  28088 2178 pp. 71-103

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

  Carlos Michelen Strofer, Jin-Long Wu, Heng Xiao, Eric Paterson

  2018-11-09

  DOI:10.4208/cicp.OA-2018-0035

  66841 6246 pp. 625-650 Open Access

• 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

  DOI:10.4208/cicp.OA-2025-0102

  243 68 pp. 27-60

• 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

  DOI:10.4208/cicp.OA-2024-0095

  5374 896 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

  DOI:10.4208/cicp.OA-2023-0162

  28544 2086 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

  DOI:10.4208/cicp.OA-2023-0075

  32040 2870 pp. 1133-1176

• 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

  DOI:10.4208/cicp.OA-2022-0284

  36494 2927 pp. 1090-1105

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

  Shamsulhaq Basir

  2023-06-06

  DOI:10.4208/cicp.OA-2022-0239

  41861 3031 pp. 1240-1269

• 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

  DOI:10.4208/cicp.OA-2023-0121

  29907 2823 pp. 1-37

• Nonlinear Reduced DNN Models for State Estimation

  Wolfgang Dahmen, Min Wang, Zhu Wang

  2022-07-06

  DOI:10.4208/cicp.OA-2021-0217

  42942 3772 pp. 1-40

• 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

  DOI:10.4208/cicp.OA-2020-0241

  48141 3150 pp. 820-850

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

  Chao Ma, Jianchun Wang, Weinan E

  2018-12-08

  DOI:10.4208/cicp.OA-2018-0269

  59477 5373 pp. 947-962 Open Access

• Deep Network Approximation Characterized by Number of Neurons

  Zuowei Shen, Haizhao Yang, Shijun Zhang

  2020-11-18

  DOI:10.4208/cicp.OA-2020-0149

  69204 3704 pp. 1768-1811

• Finite Neuron Method and Convergence Analysis

  Jinchao Xu

  2020-11-18

  DOI:10.4208/cicp.OA-2020-0191

  70604 3843 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

  DOI:10.4208/cicp.OA-2020-0179

  74201 3754 pp. 1970-2001