Search Results

• A Symplectic Based Neural Network Algorithm for Quantum Controls under Uncertainty

  Jingshi Li, Song Chen, Lijin Wang, Yanzhao Cao

  2022-05-06

  43541 3322 Pages:1525-1545

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

  Haoxiang Huang, Vigor Yang, Yingjie Liu

  2023-09-04

  35379 2818 Pages:290-317

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

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

  2024-10-29

  146 60 Pages:1090-1112

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

  Taeyoung Kim, Myungjoo Kang

  2025-09-02

  204 76 Pages:420-456

• 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

  26134 2223 Pages:467-497

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

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

  2022-08-11

  303702 3397 Pages:336-363

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

  Jianguo Huang, Haohao Wu, Tao Zhou

  2025-11-28

  913 40 Pages:553-577

• Generalized Lagrangian Neural Networks

  Shanshan Xiao, Jiawei Zhang, Yifa Tang

  2025-11-07

  2615 132 Pages:59-77

• A Network Based Approach for Unbalanced Optimal Transport on Surfaces

  Jiangong Pan, Wei Wan, Yuejin Zhang, Chenlong Bao, Zuoqiang Shi

  2025-08-23

  6018 382 Pages:661-683

• Adaptive Basis-Inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features

  Ke Li, Yaqin Zhang, Yunqing Huang, Chenyue Xie, Xueshuang Xiang

  2025-09-18

  4093 279 Pages:1453-1497

• 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

  147761 6053 Pages:2002-2041

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

  Zhipeng Chang, Ke Li, Xiufen Zou, Xueshuang Xiang

  2022-01-27

  46031 3436 Pages:370-397

• 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

  47116 3336 Pages:1453-1473

• 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

  181 59 Pages:651-672

• Convolution Neural Network Shock Detector for Numerical Solution of Conservation Laws

  Zheng Sun, Shuyi Wang, Lo-Bin Chang, Yulong Xing, Dongbin Xiu

  2020-11-18

  63767 3554 Pages:2075-2108

• A New Function Space from Barron Class and Application to Neural Network Approximation

  Yan Meng, Pingbing Ming

  2023-01-24

  38648 3386 Pages:1361-1400

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

  Tiangang Cui, Zhongjian Wang, Zhiwen Zhang

  2023-11-08

  30734 2548 Pages:934-954

• PFNN-2: A Domain Decomposed Penalty-Free Neural Network Method for Solving Partial Differential Equations

  Hailong Sheng, Chao Yang

  2022-10-28

  46910 3260 Pages:980-1006

• 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

  36587 1889 Pages:1155-1193

• 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

  88478 4440 Pages:2042-2074

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

  Yingzhou Li, Xiuyuan Cheng, Jianfeng Lu

  2020-11-18

  63549 3432 Pages:1838-1885

• 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

  36233 2866 Pages:1090-1105

• 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

  5046 565 Pages: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

  28295 2001 Pages: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

  31686 2665 Pages:1133-1176

• 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

  306975 3553 Pages:299-335

• 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

  51825 3084 Pages:1272-1295