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A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition 期刊论文
JOURNAL OF COMPUTATIONAL PHYSICS, 2022, 卷号: 461, 页码: 17
Authors:  Zhao, Yue;  Mao, Zhiping;  Guo, Ling;  Tang, Yifa;  Karniadakis, George Em
Favorite  |  View/Download：28/0  |  Submit date：2023/02/07
Uncertainty quantification  Anomalous transport  Quasi Monte Carlo simulation  Generalized polynomial chaos  Long-time integration  Poly-fractonomials  
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators 期刊论文
NATURE MACHINE INTELLIGENCE, 2021, 卷号: 3, 期号: 3, 页码: 218-+
Authors:  Lu, Lu;  Jin, Pengzhan;  Pang, Guofei;  Zhang, Zhongqiang;  Karniadakis, George Em
Favorite  |  View/Download：173/0  |  Submit date：2021/06/01
SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems 期刊论文
NEURAL NETWORKS, 2020, 卷号: 132, 页码: 166-179
Authors:  Jin, Pengzhan;  Zhang, Zhen;  Zhu, Aiqing;  Tang, Yifa;  Karniadakis, George Em
Favorite  |  View/Download：118/0  |  Submit date：2021/04/26
Deep learning  Physics-informed  Dynamical systems  Hamiltonian systems  Symplectic maps  Symplectic integrators  
Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness 期刊论文
NEURAL NETWORKS, 2020, 卷号: 130, 页码: 85-99
Authors:  Jin, Pengzhan;  Lu, Lu;  Tang, Yifa;  Karniadakis, George Em
Favorite  |  View/Download：95/0  |  Submit date：2021/01/14
Neural networks  Generalization error  Learnability  Data distribution  Cover complexity  Neural network smoothness