| DeepXDE: A deep learning library for solving differential equations L Lu, X Meng, Z Mao, GE Karniadakis SIAM review 63 (1), 208-228, 2021 | 2845 | 2021 |
| Physics-informed neural networks (PINNs) for fluid mechanics: A review S Cai, Z Mao, Z Wang, M Yin, GE Karniadakis Acta Mechanica Sinica 37 (12), 1727-1738, 2021 | 2275 | 2021 |
| Physics-informed neural networks for high-speed flows Z Mao, AD Jagtap, GE Karniadakis Computer Methods in Applied Mechanics and Engineering 360, 112789, 2020 | 1493 | 2020 |
| 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 | 676 | 2022 |
| What is the fractional Laplacian? A Lischke, G Pang, M Gulian, F Song, C Glusa, X Zheng, Z Mao, W Cai, ... arXiv preprint arXiv:1801.09767, 2018 | 623* | 2018 |
| Physics-informed neural networks for inverse problems in supersonic flows AD Jagtap, Z Mao, N Adams, GE Karniadakis Journal of Computational Physics 466, 111402, 2022 | 406 | 2022 |
| DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators Z Mao, L Lu, O Marxen, TA Zaki, GE Karniadakis Journal of computational physics 447, 110698, 2021 | 212 | 2021 |
| Analysis and approximation of a fractional Cahn--Hilliard equation M Ainsworth, Z Mao SIAM Journal on Numerical Analysis 55 (4), 1689-1718, 2017 | 190 | 2017 |
| Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations Z Mao, S Chen, J Shen Applied Numerical Mathematics 106, 165-181, 2016 | 111 | 2016 |
| Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving partial differential equations with sharp solutions Z Mao, X Meng Applied Mathematics and Mechanics 44 (7), 1069-1084, 2023 | 110 | 2023 |
| Efficient spectral–Galerkin methods for fractional partial differential equations with variable coefficients Z Mao, J Shen Journal of Computational Physics 307, 243-261, 2016 | 108 | 2016 |
| A spectral method (of exponential convergence) for singular solutions of the diffusion equation with general two-sided fractional derivative Z Mao, GE Karniadakis SIAM Journal on Numerical Analysis 56 (1), 24-49, 2018 | 101 | 2018 |
| Hermite spectral methods for fractional PDEs in unbounded domains Z Mao, J Shen SIAM Journal on Scientific Computing 39 (5), A1928-A1950, 2017 | 88 | 2017 |
| A generalized spectral collocation method with tunable accuracy for fractional differential equations with end-point singularities F Zeng, Z Mao, GE Karniadakis SIAM Journal on Scientific Computing 39 (1), A360-A383, 2017 | 78 | 2017 |
| Learning functional priors and posteriors from data and physics X Meng, L Yang, Z Mao, J del Águila Ferrandis, GE Karniadakis Journal of Computational Physics 457, 111073, 2022 | 69 | 2022 |
| Well-posedness of the Cahn–Hilliard equation with fractional free energy and its Fourier Galerkin approximation M Ainsworth, Z Mao Chaos, Solitons & Fractals 102, 264-273, 2017 | 63 | 2017 |
| Spectral element method with geometric mesh for two-sided fractional differential equations Z Mao, J Shen Advances in Computational Mathematics 44 (3), 745-771, 2018 | 44 | 2018 |
| Multi-domain spectral collocation method for variable-order nonlinear fractional differential equations T Zhao, Z Mao, GE Karniadakis Computer Methods in Applied Mechanics and Engineering 348, 377-395, 2019 | 35 | 2019 |
| Fractional Burgers equation with nonlinear non-locality: Spectral vanishing viscosity and local discontinuous Galerkin methods Z Mao, GE Karniadakis Journal of Computational Physics 336, 143-163, 2017 | 32 | 2017 |
| Nonlocal flocking dynamics: learning the fractional order of PDEs from particle simulations Z Mao, Z Li, GE Karniadakis Communications on Applied Mathematics and Computation 1 (4), 597-619, 2019 | 29 | 2019 |
George Em KarniadakisThe Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics and EngineeringVerified email at brown.edu
