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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-+
作者:  Lu, Lu;  Jin, Pengzhan;  Pang, Guofei;  Zhang, Zhongqiang;  Karniadakis, George Em
收藏  |  浏览/下载：233/0  |  提交时间：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
作者:  Jin, Pengzhan;  Zhang, Zhen;  Zhu, Aiqing;  Tang, Yifa;  Karniadakis, George Em
收藏  |  浏览/下载：176/0  |  提交时间：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
作者:  Jin, Pengzhan;  Lu, Lu;  Tang, Yifa;  Karniadakis, George Em
收藏  |  浏览/下载：150/0  |  提交时间：2021/01/14
Neural networks  Generalization error  Learnability  Data distribution  Cover complexity  Neural network smoothness  
Numerical simulation of an immersed rotating structure in fluid for hemodynamic applications 期刊论文
JOURNAL OF COMPUTATIONAL SCIENCE, 2019, 卷号: 30, 页码: 79-89
作者:  Leng, Wei;  Zhang, Chen-Song;  Sun, Pengtao;  Gao, Bin;  Xu, Jinchao
收藏  |  浏览/下载：210/0  |  提交时间：2019/03/11
Artificial heart pump  Fluid-structure interactions  Monolithic method  Arbitrary Lagrangian-Eulerian formulation  Mixed finite element  
Regularized HSS iteration methods for saddle-point linear systems 期刊论文
BIT NUMERICAL MATHEMATICS, 2017, 卷号: 57, 期号: 2, 页码: 287-311
作者:  Bai, Zhong-Zhi;  Benzi, Michele
收藏  |  浏览/下载：163/0  |  提交时间：2018/07/30
Saddle-point linear system  Hermitian and skew-Hermitian splitting  Iterative methods  Inexact implementation  Preconditioning  Convergence  
Optimization of Multi-Fidelity Computer Experiments via the EQIE Criterion 期刊论文
TECHNOMETRICS, 2017, 卷号: 59, 期号: 1, 页码: 58-68
作者:  He, Xu;  Tuo, Rui;  Wu, C. F. Jeff
收藏  |  浏览/下载：129/0  |  提交时间：2018/07/30
Design of experiment  Expected improvement criterion  Gaussian process model  Kriging  Multi-fidelity experiment  
A comparison of two Stokes ice sheet models applied to the Marine Ice Sheet Model Intercomparison Project for plan view models (MISMIP3d) 期刊论文
CRYOSPHERE, 2017, 卷号: 11, 期号: 1, 页码: 179-190
作者:  Zhang, Tong;  Price, Stephen;  Ju, Lili;  Leng, Wei;  Brondex, Julien;  Durand, Gael;  Gagliardini, Olivier
收藏  |  浏览/下载：157/0  |  提交时间：2018/07/30
A new parallelization scheme for adaptive mesh refinement 期刊论文
JOURNAL OF COMPUTATIONAL SCIENCE, 2016, 卷号: 16, 页码: 79-88
作者:  Loffler, Frank;  Cao, Zhoujian;  Brandt, Steven R.;  Du, Zhihui
收藏  |  浏览/下载：164/0  |  提交时间：2018/07/30
Parallel application frameworks  Parallel algorithms  Parallel applications  Adaptive mesh refinement  
A CENTRAL LIMIT THEOREM FOR NESTED OR SLICED LATIN HYPERCUBE DESIGNS 期刊论文
STATISTICA SINICA, 2016, 卷号: 26, 期号: 3, 页码: 1117-1128
作者:  He, Xu;  Qian, Peter Z. G.
收藏  |  浏览/下载：123/0  |  提交时间：2018/07/30
Computer experiment  design of experiment  method of moments  numerical integration  uncertainty quantification  
A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties 期刊论文
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2016, 卷号: 4, 期号: 1, 页码: 767-795
作者:  Tuo, Rui;  Wu, C. F. Jeff
收藏  |  浏览/下载：152/0  |  提交时间：2018/07/30
computer experiments  uncertainty quantification  Gaussian process  reproducing kernel Hilbert space