Search Results

• 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

  16 9 Pages:1-26

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

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

  2025-08-23

  6662 629 Pages:603-629

• 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

  29895 2817 Pages:1-37

• 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

  32024 2860 Pages:1133-1176

• Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation

  Min Cai, Ehsan Kharazmi, Changpin Li, George Em Karniadakis

  2022-01-27

  44503 3310 Pages:331-369

• 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

  151264 6957 Pages:2002-2041

• 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

  89495 4608 Pages:2042-2074

• Dying ReLU and Initialization: Theory and Numerical Examples

  Lu Lu, Yeonjong Shin, Yanhui Su, George Em Karniadakis

  2020-11-18

  86122 4189 Pages:1671-1706

• Analytical and Computational Studies of Correlations of Hydrodynamic Fluctuations in Shear Flow

  Xin Bian, Mingge Deng, George Em Karniadakis

  2018-07-03

  47042 5263 Pages:93-117

• Extrapolation-Based Acceleration of Iterative Solvers: Application to Simulation of 3D Flows

  Leopold Grinberg, George Em Karniadakis

  2011-03-05

  39682 4199 Pages:607-626

• Error Control in Multi-Element Generalized Polynomial Chaos Method for Elliptic Problems with Random Coefficients

  Xiaoliang Wan, George Em Karniadakis

  2018-04-11

  41373 3603 Pages:793-820

• A Scalable Domain Decomposition Method for Ultra-Parallel Arterial Flow Simulations

  Leopold Grinberg, George Em Karniadakis

  2008-11-05

  36745 4097 Pages:1151-1169