Search Results

• 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

  49367 4042 Pages:188-223

• Continuous-Variable Deep Quantum Neural Networks for Flexible Learning of Structured Classical Information

  Jasvith Raj Basani, Aranya Bhattacherjee

  2021-08-10

  46210 2995 Pages:1216-1231

• 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

  86027 4254 Pages:1746-1767

• Time Integration Schemes Based on Neural Networks for Solving Partial Differential Equations on Coarse Grids

  Xinxin Yan, Zhideng Zhou, Xiaohan Cheng, Xiaolei Yang

  2024-12-02

  15876 1169 Pages:1262-1306

• Generalization Error in the Deep Ritz Method with Smooth Activation Functions

  Janne Siipola

  2024-04-10

  24248 2315 Pages:761-815 Open-access

• A Rate of Convergence of Weak Adversarial Neural Networks for the Second Order Parabolic PDEs

  Yuling Jiao, Jerry Zhijian Yang, Cheng Yuan, Junyu Zhou

  2023-10-07

  35482 2884 Pages:813-836

• Learning Specialized Activation Functions for Physics-Informed Neural Networks

  Honghui Wang, Lu Lu, Shiji Song, Gao Huang

  2023-11-08

  34553 2896 Pages:869-906

• Towards the Efficient Calculation of Quantity of Interest from Steady Euler Equations II: A CNNs-Based Automatic Implementation

  Jingfeng Wang, Guanghui Hu

  2026-01-03

  1687 47 Pages:884-918

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

  Zhipeng Chang, Ke Li, Xiufen Zou, Xueshuang Xiang

  2022-01-27

  46148 3482 Pages:370-397

• Convergence Rate Analysis for Deep Ritz Method

  Chenguang Duan, Yuling Jiao, Yanming Lai, Dingwei Li, Xiliang Lu, Jerry Zhijian Yang

  2022-03-30

  58970 3389 Pages:1020-1048

• Convergence Analysis for Over-Parameterized Deep Learning

  Yuling Jiao, Xiliang Lu, Peiying Wu, Jerry Zhijian Yang

  2024-07-29

  27948 2069 Pages:71-103

• Data-Driven, Physics-Based Feature Extraction from Fluid Flow Fields Using Convolutional Neural Networks

  Carlos Michelén Ströfer, Jin-Long Wu, Heng Xiao & Eric Paterson

  2018-11-09

  66627 6161 Pages:625-650 Open-access

• 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

  5235 749 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

  28423 2043 Pages:1120-1154

• 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

  36361 2889 Pages:1090-1105

• 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

  31843 2797 Pages:1133-1176

• Model Reduction with Memory and the Machine Learning of Dynamical Systems

  Chao Ma, Jianchun Wang & Weinan E

  2018-12-08

  59290 5263 Pages:947-962 Open-access

• Splitting Physics-Informed Neural Networks for Inferring the Dynamics of Integer- and Fractional-Order Neuron Models

  Simin Shekarpaz, Fanhai Zeng, George Karniadakis

  2024-01-31

  29757 2732 Pages:1-37

• Deep Network Approximation Characterized by Number of Neurons

  Zuowei Shen, Haizhao Yang, Shijun Zhang

  2020-11-18

  68957 3646 Pages:1768-1811

• An Understanding of the Physical Solutions and the Blow-up Phenomenon for Nonlinear Noisy Leaky Integrate and Fire Neuronal Models

  María J. Cáceres, Alejandro Ramos-Lora

  2021-07-01

  48052 3113 Pages:820-850

• Nonlinear Reduced DNN Models for State Estimation

  Wolfgang Dahmen, Min Wang, Zhu Wang

  2022-07-06

  42845 3718 Pages:1-40

• Investigating and Mitigating Failure Modes in Physics-Informed Neural Networks (PINNs)

  Shamsulhaq Basir

  2023-06-06

  41665 2977 Pages:1240-1269

• Neural-Network-Augmented Empirical Interpolation Method for Field Reconstruction with Noise and Vibration Tolerance

  Han Li, Helin Gong, Chuanju Xu

  2026-01-03

  1680 44 Pages:855-883

• Finite Neuron Method and Convergence Analysis

  Jinchao Xu

  2020-11-18

  70404 3799 Pages:1707-1745

• Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains

  Ziqi Liu, Wei Cai, Zhi-Qin John Xu

  2020-11-18

  73856 3682 Pages:1970-2001

• MHDnet: Physics-Preserving Learning for Solving Magnetohydrodynamics Problems

  Xiaofei Guan, Boya Hu, Shipeng Mao, Xintong Wang, Zihao Yang

  2024-10-29

  21671 1212 Pages:943-976

• Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability

  Zhen Gao, Qi Liu, Jan S. Hesthaven, Bao-Shan Wang, Wai Sun Don, Xiao Wen

  2021-04-30

  49968 4514 Pages:97-123