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

  DOI:10.4208/cicp.OA-2019-0168

  52032 3444 pp. 379-411

• 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

• 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

• Frame Invariance and Scalability of Neural Operators for Partial Differential Equations

  Muhammad I. Zafar, Jiequn Han, Xu-Hui Zhou, Heng Xiao

  2022-08-11

  DOI:10.4208/cicp.OA-2021-0256

  303899 3517 pp. 336-363

• A Neural Network Approach to Sampling Based Learning Control for Quantum System with Uncertainty

  Jingshi Li, Song Chen, Yanzhao Cao, Zhao Sun

  2021-10-26

  DOI:10.4208/cicp.OA-2020-0182

  47322 3405 pp. 1453-1473

• On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

  Yeonjong Shin, Jérôme Darbon, George Em Karniadakis

  2020-11-18

  DOI:10.4208/cicp.OA-2020-0193

  89565 4614 pp. 2042-2074

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

  Liang Yan, Tao Zhou

  2020-11-18

  DOI:10.4208/cicp.OA-2020-0186

  67487 3473 pp. 2180-2205

• Physics-Driven Learning of the Steady Navier-Stokes Equations Using Deep Convolutional Neural Networks

  Hao Ma, Yuxuan Zhang, Nils Thuerey, Xiangyu Hu, Oskar J. Haidn

  2022-09-29

  DOI:10.4208/cicp.OA-2021-0146

  42895 3385 pp. 715-736

• 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

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

  Yingzhou Li, Xiuyuan Cheng, Jianfeng Lu

  2020-11-18

  DOI:10.4208/cicp.OA-2020-0214

  63895 3512 pp. 1838-1885

• Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

  Ameya D. Jagtap, George Em Karniadakis

  2020-11-18

  DOI:10.4208/cicp.OA-2020-0164

  151550 6990 pp. 2002-2041

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

  Colby L. Wight, Jia Zhao

  2021-01-13

  DOI:10.4208/cicp.OA-2020-0086

  59575 3990 pp. 930-954

• 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

  DOI:10.4208/cicp.OA-2021-0186

  52182 3175 pp. 1272-1295

• 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

• 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 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

• 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

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

  Yulei Liao, Pingbing Ming

  2021-03-24

  DOI:10.4208/cicp.OA-2020-0219

  53501 3565 pp. 1365-1384

• Deep Learning-Based Computational Method for Soft Matter Dynamics: Deep Onsager-Machlup Method

  Zhihao Li, Boyi Zou, Haiqin Wang, Jian Su, Dong Wang, Xinpeng Xu

  2025-09-02

  DOI:10.4208/cicp.OA-2023-0294

  11909 813 pp. 353-382

• Asymptotic-Preserving Neural Networks for Multiscale Kinetic Equations

  Shi Jin, Zheng Ma, Keke Wu

  2024-04-10

  DOI:10.4208/cicp.OA-2023-0211

  25513 2191 pp. 693-723

• 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

• 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

• 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

• 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

  DOI:10.4208/cicp.OA-2020-0142

  55435 3561 pp. 698-728

• Deep Learning-Based Reduced-Order Methods for Fast Transient Dynamics

  Martina Cracco, Giovanni Stabile, Andrea Lario, Armin Sheidani, Martin Larcher, Folco Casadei, Georgios Valsamos, Gianluigi Rozza

  2026-01-03

  DOI:10.4208/cicp.OA-2024-0168

  2158 190 pp. 635-660

• Deep Unfitted Nitsche Method for Elliptic Interface Problems

  Hailong Guo, Xu Yang

  2022-03-30

  DOI:10.4208/cicp.OA-2021-0201

  52740 3338 pp. 1162-1179

• 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