Search Results

• Loss Jump During Loss Switch in Solving PDEs with Neural Networks

  Zhiwei Wang, Lulu Zhang, Zhongwang Zhang, Zhi-Qin John Xu

  2024-10-29

  DOI:10.4208/cicp.OA-2024-0096

  17522 1208 pp. 1090-1112

• Generalized Lagrangian Neural Networks

  Shanshan Xiao, Jiawei Zhang, Yifa Tang

  2026-01-15

  DOI:10.4208/cicp.OA-2024-0052

  3372 511 pp. 59-77

• 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 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

• 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

• Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems

  Sidi Wu, Aiqing Zhu, Yifa Tang, Benzhuo Lu

  2023-03-13

  DOI:10.4208/cicp.OA-2022-0218

  41082 3304 pp. 596-627

• 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

• 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

• 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

• 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 Mixed Wavelet-Learning Method of Predicting Macroscopic Effective Heat Transfer Conductivities of Braided Composite Materials

  Hao Dong, Wenbo Kou, Junyan Han, Jiale Linghu, Minqiang Zou, Junzhi Cui

  2022-01-27

  DOI:10.4208/cicp.OA-2021-0110

  43172 3277 pp. 593-625

• Two-Scale Neural Networks for Partial Differential Equations with Small Parameters

  Qiao Zhuang, Chris Ziyi Yao, Zhongqiang Zhang, George Em Karniadakis

  2025-08-23

  DOI:10.4208/cicp.OA-2024-0040

  6671 631 pp. 603-629

• 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

• 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

• 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

• 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

• Score-fPINN: Fractional Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck-Lévy Equations

  Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis, Kenji Kawaguchi

  2026-04-10

  DOI:10.4208/cicp.OA-2024-0201

  170 55 pp. 1-26

• 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

• Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws, Part II: 2D Problems

  Haoxiang Huang, Vigor Yang, Yingjie Liu

  2023-11-08

  DOI:10.4208/cicp.OA-2023-0026

  77238 3710 pp. 907-933

• 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

• 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

• Scale-Decomposed Physics-Informed Neural Networks for Singular Perturbation Problems

  Lei Zhang, Guowei He

  2026-01-18

  DOI:10.4208/cicp.OA-2024-0149

  1056 238 pp. 1267-1298

• A Model-Data Asymptotic-Preserving Neural Network Method Based on Micro-Macro Decomposition for Gray Radiative Transfer Equations

  Hongyan Li, Song Jiang, Wenjun Sun, Liwei Xu, Guanyu Zhou

  2024-06-14

  DOI:10.4208/cicp.OA-2022-0315

  36826 1981 pp. 1155-1193

• Adaptive Neural Network Basis Methods for Partial Differential Equations with Low-Regular Solutions

  Jianguo Huang, Haohao Wu, Tao Zhou

  2026-02-15

  DOI:10.4208/cicp.OA-2024-0310

  4085 195 pp. 553-577

• Learning Invariant Representation of Multiscale Hyperelastic Constitutive Law from Sparse Experimental Data

  Rui He, Junzhi Cui, Zihao Yang, Jieqiong Zhang, Xiaofei Guan

  2023-09-04

  DOI:10.4208/cicp.OA-2023-0098

  34260 2839 pp. 392-417

• 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 Neural Particle Method with Interface Tracking and Adaptive Particle Refinement for Free Surface Flows

  Pei-Hsin Pai, Heng-Chuan Kan, Hock-Kiet Wong, Yih-Chin Tai

  2024-10-29

  DOI:10.4208/cicp.OA-2023-0235

  17866 1218 pp. 1021-1052