Search Results

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

  Taeyoung Kim, Myungjoo Kang

  2025-09-02

  12147 810 Pages: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

  40907 3253 Pages:596-627

• 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

  89003 4556 Pages:2042-2074

• 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

  10567 630 Pages:603-622

• Solving Allen-Cahn and Cahn-Hilliard Equations Using the Adaptive Physics Informed Neural Networks

  Colby L. Wight, Jia Zhao

  2021-01-13

  59168 3906 Pages:930-954

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

  Lei Zhang, Guowei He

  2026-01-18

  368 76 Pages:1267-1298

• 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

  149394 6595 Pages:2002-2041

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

  Haoxiang Huang, Vigor Yang, Yingjie Liu

  2023-09-04

  35522 2848 Pages:290-317

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

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

  2025-08-23

  6514 584 Pages:603-629

• 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

  51988 3131 Pages:1272-1295

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

  Haoxiang Huang, Vigor Yang, Yingjie Liu

  2023-11-08

  77084 3664 Pages:907-933

• 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

  36696 1938 Pages:1155-1193

• 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

  17729 1163 Pages:1021-1052

• 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

  26287 2282 Pages:467-497

• 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

• 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

• 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

• 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

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

  Shamsulhaq Basir

  2023-06-06

  41665 2977 Pages:1240-1269

• Convergence Analysis of PINNs with Over-Parameterization

  Mo Chen, Zhao Ding, Yuling Jiao, Xiliang Lu, Peiying Wu, Jerry Zhijian Yang

  2025-04-27

  9192 531 Pages:942-974

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

  Jihong Wang, Xin Wang, Jing Li, Bin Liu

  2025-05-29

  8885 481 Pages:1383-1416

• Integral Regularization PINNs for Evolution Equations

  Xiaodong Feng, Haojiong Shangguan, Tao Tang, Xiaoliang Wan

  2026-02-15

  3808 139 Pages:356-386