教育经历：

2009.09-2015.06，伟德国际1946源自英国计算数学，博士

2005.10-2009.06，重庆大学信息与计算科学专业，学士

工作经历：

2020.11至今，伟德国际1946源自英国教授

2020.10-2020.11，伟德国际1946源自英国副教授

2015.10-2020.09，美国布朗大学应用数学系博士后

研究方向：

微分方程数值解，深度学习，相场模型

授课情况：

2020-2021春季学期，微积分V-2

论文：

* means corresponding author.

1. L. Lu, X. Meng, Z. Mao and G.E. Karniadakis, DeepXDE: A deep learning library for solving differential equations, SIAM Review, 2021, 63(1), pp.208-228.

2. Z. Mao, A.D. Jagtap and G.E. Karniadakis, Physics-informed neural networks for high-speed flows, Computer Methods in Applied Mechanics and Engineering, 2020, 360, pp. 112789.

3. M. Ainsworth and Z. Mao*, Fractional phase field crystal modelling: Analysis, approximation and pattern formation, IMA Journal of Applied Mathematics, 85 (2), pp. 231-262.

4. X. Li, Z. Mao*, F. Song, H. Wang and G.E. Karniadakis, A fast solver for spectral element approximation applied to fractional differential equations using hierarchical matrix approximation, Computer Methods in Applied Mechanics and Engineering, 2020 366, pp. 113053.

5. A. Lischke, G. Pang, M. Gulian, F. Song, C. Glusa, X. Zheng, Z. Mao, W. Cai, M.M. Meerschaert, M. Ainsworth and G. E. Karniadakis, What is the Fractional Laplacian? A Comparative Review with New Results, Journal of Computational Physics, 2020, 404, pp. 109009.

6. M. Ainsworth and Z. Mao, Phase field crystal based prediction of temperature and density dependence of elastic constants through structural phase transition, Physical Review B, 2019, 100(10), pp. 104101.

7. Z. Mao, Z. Li and G.E. Karniadakis, Nonlocal flocking dynamics: {L}earning the fractional order of PDEs from particle simulations, Communication on Applied Mathematics and Computation, 2019, 1(4), pp. 597-619.

8. M. Ainsworth and Z. Mao, Analysis and approximation of gradient flows associated with a fractional order Gross-Pitaevskii free energy, Communication on Applied Mathematics and Computation, 2019, 1 (1), pp. 5-19.

9. N. Wang, Z. Mao* and G.E. Karniadakis. A spectral penalty method for two-sided fractional differential equations with general boundary conditions, SIAM Journal on Scientific Computing, 2019, 41 (3), A1840-A1866.

10. T. Zhao, Z. Mao* and G.E. Karniadakis, Multi-domain spectral collocation method for variable-order nonlinear fractional differential equations, Computer Methods in Applied Mechanics and Engineering, 2019 (348), 377-395.

11. Z. Mao and J. Shen, Spectral element method with geometric mesh for two-sided fractional differential equations, Advances in Computational Mathematics, 2018, 44 (3), 745-771.

12. Z. Mao* and G.E. Karniadakis, A spectral method (of exponential convergence) for singular solutions of the diffusion equation with general two-sided fractional derivative, SIAM Journal on Numerical Analysis, 2018, 56 (1), 24-49.

13. Z. Mao* and J. Shen, Hermite spectral methods for fractional PDEs in unbounded domains, SIAM Journal on Scientific Computing, 2017, 39 (5), A1928-A1950.

14. M Ainsworth, Z. Mao, Well-posedness of the Cahn-Hilliard equation with fractional free energy and its Fourier Galerkin approximation, Chaos, Solitons & Fractals, 2017, 102, 264-273.

15. M Ainsworth, Z. Mao, Analysis and approximation of a fractional Cahn-Hilliard equation, SIAM Journal on Numerical Analysis, 2017, 55 (4), 1689-1718.

16. Z. Mao and G.E. Karniadakis, Fractional Burgers equation with nonlinear non-locality: spectral vanishing viscosity and local discontinuous Galerkin methods, Journal of Computational Physics, 2017, 336, 143-163.

17. F. Zeng, Z. Mao, G.E. Karniadakis, A generalized spectral collocation method with tunable accuracy for fractional differential equations with end-point singularities, SIAM Journal on Scientific Computing, 2017, 39 (1), A360-A383.

18. Z. Mao, S Chen and J. Shen, Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations, Applied Numerical Mathematics, 2016, 106, 165-181.

19. Z. Mao and J. Shen, Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients, Journal of Computational Physics, 2016, 307, 243-261.

20. Z. Mao and J. Shen, A semi-implicit spectral deferred correction method for two water wave models with nonlocal viscous term and numerical study of their decay rates, Sci Sin Math, 2015, 45 (8), 1153-1168.