Search Results

• Machine Learning and Computational Mathematics

  Weinan E

  2020-11-18

  DOI:10.4208/cicp.OA-2020-0185

  89035 4381 pp. 1639-1670

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

  Yufei Wang, Ziju Shen, Zichao Long, Bin Dong

  2020-11-18

  DOI:10.4208/cicp.OA-2020-0194

  62676 3497 pp. 2158-2179

• Finding the Origin of Noise Transients in LIGO Data with Machine Learning

  Marco Cavaglia, Kai Staats, Teerth Gill

  2018-12-08

  DOI:10.4208/cicp.OA-2018-0092

  56918 4867 pp. 963-987 Open Access

• 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

• A Data-Driven Random Subfeature Ensemble Learning Algorithm for Weather Forecasting

  Chen Yu, Haochen Li, Jiangjiang Xia, Hanqiuzi Wen, Pingwen Zhang

  2020-08-27

  DOI:10.4208/cicp.OA-2020-0006

  50863 3346 pp. 1305-1320

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

  Jihong Wang, Xin Wang, Jing Li, Bin Liu

  2025-05-29

  DOI:10.4208/cicp.OA-2023-0327

  9043 520 pp. 1383-1416

• A Consensus-Based Global Optimization Method with Adaptive Momentum Estimation

  Jingrun Chen, Shi Jin, Liyao Lyu

  2022-03-30

  DOI:10.4208/cicp.OA-2021-0144

  47297 3061 pp. 1296-1316

• 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

• 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

  DOI:10.4208/cicp.OA-2024-0066

  15993 1010 pp. 30-60

• Physically Guided Neural Network Based on Transfer Learning (TL-PGNN) for Hypersonic Heat Flux Prediction

  Biao Chen, Jifa Zhang, Shuai Zhang, Xiaoxiao Song, Yao Zheng

  2024-10-09

  DOI:10.4208/cicp.OA-2023-0308

  16084 1298 pp. 651-672

• 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

• Solving Time Dependent Fokker-Planck Equations via Temporal Normalizing Flow

  Xiaodong Feng, Li Zeng, Tao Zhou

  2022-08-11

  DOI:10.4208/cicp.OA-2022-0090

  308990 3594 pp. 401-423

• 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

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

  Jayeon Joo, Dongseok Kim, Hojun You, Chongam Kim

  2024-12-02

  DOI:10.4208/cicp.OA-2024-0063

  16042 1207 pp. 1307-1338

• MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs

  Lulu Zhang, Tao Luo, Yaoyu Zhang, Weinan E, Zhi-Qin John Xu, Zheng Ma

  2022-08-11

  DOI:10.4208/cicp.OA-2021-0257

  307217 3645 pp. 299-335

• Approximating Numerical Fluxes Using Fourier Neural Operators for Hyperbolic Conservation Laws

  Taeyoung Kim, Myungjoo Kang

  2025-09-02

  DOI:10.4208/cicp.OA-2024-0123

  12321 905 pp. 420-456

• Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-Informed Neural Networks Framework for Interface Problems

  Sumanta Roy, Chandrasekhar Annavarapu, Pratanu Roy, Antareep Kumar Sarma

  2025-09-02

  DOI:10.4208/cicp.OA-2024-0131

  10784 686 pp. 603-622

• Preface

  2020-11-18

  382 105 pp. i-i

• 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

• Enforcing Imprecise Constraints on Generative Adversarial Networks for Emulating Physical Systems

  Yang Zeng, Jin-Long Wu, Heng Xiao

  2021-07-01

  DOI:10.4208/cicp.OA-2020-0106

  49410 3307 pp. 635-665

• 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

• 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

• Generalization Error Analysis of Neural Networks with Gradient Based Regularization

  Lingfeng Li, Xue-Cheng Tai, Jiang Yang

  2022-10-28

  DOI:10.4208/cicp.OA-2021-0211

  45822 3323 pp. 1007-1038

• Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws, Part I: 1D Problems

  Haoxiang Huang, Vigor Yang, Yingjie Liu

  2023-09-04

  DOI:10.4208/cicp.OA-2022-0285

  35668 2891 pp. 290-317

• High-Dimensional Nonlinear Multi-Fidelity Model with Gradient-Free Active Subspace Method

  Bangde Liu, Guang Lin

  2020-11-18

  DOI:10.4208/cicp.OA-2020-0195

  62704 3396 pp. 1937-1969

• 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