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Zhongqiang Zhang
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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
L Lu, P Jin, G Pang, Z Zhang, GE Karniadakis
Nature machine intelligence 3 (3), 218-229, 2021
13612021
hp-VPINNs: Variational physics-informed neural networks with domain decomposition
E Kharazmi, Z Zhang, GE Karniadakis
Computer Methods in Applied Mechanics and Engineering 374, 113547, 2021
4422021
A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data
L Lu, X Meng, S Cai, Z Mao, S Goswami, Z Zhang, GE Karniadakis
Computer Methods in Applied Mechanics and Engineering 393, 114778, 2022
3012022
Variational physics-informed neural networks for solving partial differential equations
E Kharazmi, Z Zhang, GE Karniadakis
arXiv preprint arXiv:1912.00873, 2019
2852019
A fundamental mean-square convergence theorem for SDEs with locally Lipschitz coefficients and its applications
MV Tretyakov, Z Zhang
SIAM Journal on Numerical Analysis 51 (6), 3135-3162, 2013
1822013
Numerical methods for stochastic partial differential equations with white noise
Z Zhang, GE Karniadakis
Springer, 2017
1522017
A generalized spectral collocation method with tunable accuracy for variable-order fractional differential equations
F Zeng, Z Zhang, GE Karniadakis
SIAM Journal on Scientific Computing 37 (6), A2710-A2732, 2015
1382015
Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions
F Zeng, Z Zhang, GE Karniadakis
Computer Methods in Applied Mechanics and Engineering 327, 478-502, 2017
1282017
Error estimates of residual minimization using neural networks for linear PDEs
Y Shin, Z Zhang, GE Karniadakis
Journal of Machine Learning for Modeling and Computing 4 (4), 2023
802023
Implicit-explicit difference schemes for nonlinear fractional differential equations with nonsmooth solutions
W Cao, F Zeng, Z Zhang, GE Karniadakis
SIAM Journal on Scientific Computing 38 (5), A3070-A3093, 2016
772016
Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations
F Zeng, Z Zhang, GE Karniadakis
Journal of Computational Physics 307, 15-33, 2016
712016
Spectral and discontinuous spectral element methods for fractional delay equations
M Zayernouri, W Cao, Z Zhang, GE Karniadakis
SIAM Journal on Scientific Computing 36 (6), B904-B929, 2014
702014
Numerical Methods for Stochastic Delay Differential Equations Via the Wong--Zakai Approximation
W Cao, Z Zhang, GE Karniadakis
SIAM Journal on Scientific Computing 37 (1), A295-A318, 2015
622015
Optimal error estimates of spectral Petrov--Galerkin and collocation methods for initial value problems of fractional differential equations
Z Zhang, F Zeng, GE Karniadakis
SIAM Journal on Numerical Analysis 53 (4), 2074-2096, 2015
562015
Optimal regularity and error estimates of a spectral Galerkin method for fractional advection-diffusion-reaction equations
Z Hao, Z Zhang
SIAM Journal on Numerical Analysis 58 (1), 211-233, 2020
532020
Fractional centered difference scheme for high-dimensional integral fractional Laplacian
Z Hao, Z Zhang, R Du
Journal of Computational Physics 424, 109851, 2021
482021
Error estimates for the ANOVA method with polynomial chaos interpolation: Tensor product functions
Z Zhang, M Choi, GE Karniadakis
SIAM Journal on Scientific Computing 34 (2), A1165-A1186, 2012
412012
Anchor points matter in ANOVA decomposition
Z Zhang, M Choi, GE Karniadakis
Spectral and High Order Methods for Partial Differential Equations: Selected …, 2011
402011
Convergence rate of DeepONets for learning operators arising from advection-diffusion equations
B Deng, Y Shin, L Lu, Z Zhang, GE Karniadakis
arXiv preprint arXiv:2102.10621, 2021
372021
Time-splitting schemes for fractional differential equations I: smooth solutions
W Cao, Z Zhang, GE Karniadakis
SIAM Journal on Scientific Computing 37 (4), A1752-A1776, 2015
352015
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