| 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 | 2155 | 2021 |
| 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 | 608 | 2021 |
| 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 | 451 | 2022 |
| Variational physics-informed neural networks for solving partial differential equations E Kharazmi, Z Zhang, GE Karniadakis arXiv preprint arXiv:1912.00873, 2019 | 382 | 2019 |
| 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 | 199 | 2013 |
| Numerical methods for stochastic partial differential equations with white noise Z Zhang, GE Karniadakis Springer, 2017 | 172 | 2017 |
| 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 | 150 | 2015 |
| 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 | 135 | 2017 |
| 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 | 108 | 2023 |
| 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 | 85 | 2016 |
| 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 | 74 | 2016 |
| 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 | 71 | 2014 |
| Approximation rates of DeepONets for learning operators arising from advection–diffusion equations B Deng, Y Shin, L Lu, Z Zhang, GE Karniadakis Neural Networks 153, 411-426, 2022 | 66 | 2022 |
| Fractional centered difference scheme for high-dimensional integral fractional Laplacian Z Hao, Z Zhang, R Du Journal of Computational Physics 424, 109851, 2021 | 66 | 2021 |
| 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 | 66 | 2015 |
| 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 | 60 | 2020 |
| 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 | 57 | 2015 |
| 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 | 48 | 2021 |
| 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 | 39 | 2012 |
| Error estimates of spectral Galerkin methods for a linear fractional reaction–diffusion equation Z Zhang Journal of Scientific Computing 78 (2), 1087-1110, 2019 | 38 | 2019 |
George Em KarniadakisThe Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics and Engineering確認したメール アドレス: brown.edu