Search Results

• Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning

  Yufei Wang, Ziju Shen, Zichao Long, Bin Dong

  2020-11-18

  https://doi.org/10.4208/cicp.OA-2020-0194

  62322 3419 pp. 2158-2179

• Accurate Adaptive Deep Learning Method for Solving Elliptic Problems

  Jinyong Ying, Yaqi Xie, Jiao Li, Hongqiao Wang

  2025-09-02

  https://doi.org/10.4208/cicp.OA-2024-0113

  367 59 pp. 849-876

• 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

  https://doi.org/10.4208/cicp.OA-2023-0294

  263 68 pp. 353-382

• 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

• An Augmented Lagrangian Deep Learning Method for Variational Problems with Essential Boundary Conditions

  Jianguo Huang, Haoqin Wang, Tao Zhou

  2022-03-03

  https://doi.org/10.4208/cicp.OA-2021-0176

  50442 3265 pp. 966-986

• 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

• 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

• 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

• 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

  https://doi.org/10.4208/cicp.OA-2021-0146

  42625 3275 pp. 715-736

• Newton’s Method and Its Hybrid with Machine Learning for Navier-Stokes Darcy Models Discretized by Mixed Element Methods

  Jianguo Huang, Hui Peng, Haohao Wu

  2025-01-22

  https://doi.org/10.4208/cicp.OA-2024-0066

  187 97 pp. 30-60

• Data Generation-Based Operator Learning for Solving Partial Differential Equations on Unbounded Domains

  Jihong Wang, Xin Wang, Jing Li, Bin Liu

  2025-05-29

  https://doi.org/10.4208/cicp.OA-2023-0327

  194 50 pp. 1383-1416

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

  Yulei Liao, Pingbing Ming

  2021-03-24

  https://doi.org/10.4208/cicp.OA-2020-0219

  53158 3424 pp. 1365-1384

• Ensemble Gradient for Learning Turbulence Models from Indirect Observations

  Carlos A. Michelén Ströfer, Xin-Lei Zhang, Heng Xiao

  2021-10-26

  https://doi.org/10.4208/cicp.OA-2021-0082

  80569 3686 pp. 1269-1289

• 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

  https://doi.org/10.4208/cicp.OA-2021-0088

  49247 3959 pp. 188-223

• 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

• Dirichlet-Neumann Learning Algorithm for Solving Elliptic Interface Problems

  Qi Sun, Xuejun Xu, Haotian Yi

  2025-07-11

  https://doi.org/10.4208/cicp.OA-2024-0046

  5086 463 pp. 248-284

• 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

  https://doi.org/10.4208/cicp.OA-2020-0164

  147761 6053 pp. 2002-2041

• 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

• 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

• 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

  https://doi.org/10.4208/cicp.OA-2023-0072

  155 138 pp. 200-220

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

  Yingzhou Li, Xiuyuan Cheng, Jianfeng Lu

  2020-11-18

  https://doi.org/10.4208/cicp.OA-2020-0214

  63549 3432 pp. 1838-1885

• 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

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

  Bo Wang, Wenzhong Zhang, Wei Cai

  2020-11-18

  https://doi.org/10.4208/cicp.OA-2020-0192

  64184 3294 pp. 2139-2157

• A Variational Neural Network Approach for Glacier Modelling with Nonlinear Rheology

  Tiangang Cui, Zhongjian Wang, Zhiwen Zhang

  2023-11-08

  https://doi.org/10.4208/cicp.OA-2022-0272

  30734 2548 pp. 934-954

• Deep Potential: A General Representation of a Many-Body Potential Energy Surface

  Jiequn Han, Linfeng Zhang, Roberto Car & Weinan E

  2018-08-21

  https://doi.org/10.4208/cicp.OA-2017-0213

  94494 6411 pp. 629-639 Open Access

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

  Yujie Liu, Chao Yang

  2022-03-03

  https://doi.org/10.4208/cicp.OA-2021-0104

  45431 3205 pp. 739-770

• A Deep Spatio-Temporal Forecasting Model for Multi-Site Weather Prediction Post-Processing

  Wenjia Kong, Haochen Li, Chen Yu, Jiangjiang Xia, Yanyan Kang, Pingwen Zhang

  2021-12-06

  https://doi.org/10.4208/cicp.OA-2020-0158

  53419 4553 pp. 131-153