Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients. - Zhiping Mao; Jie Shen 001 (J. Comput. Phys., 2016)

Fractional Burgers equation with nonlinear non-locality: Spectral vanishing viscosity and local discontinuous Galerkin methods. - Zhiping Mao; George E. Karniadakis (J. Comput. Phys., 2017)

Analysis and Approximation of a Fractional Cahn-Hilliard Equation. - Mark Ainsworth; Zhiping Mao (SIAM J. Numer. Anal., 2017)

Hermite Spectral Methods for Fractional PDEs in Unbounded Domains. - Zhiping Mao; Jie Shen 001 (SIAM J. Sci. Comput., 2017)

A Generalized Spectral Collocation Method with Tunable Accuracy for Fractional Differential Equations with End-Point Singularities. - Fanhai Zeng; Zhiping Mao; George E. Karniadakis (SIAM J. Sci. Comput., 2017)

Spectral element method with geometric mesh for two-sided fractional differential equations. - Zhiping Mao; Jie Shen 001 (Adv. Comput. Math., 2018)

A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative. - Zhiping Mao; George E. Karniadakis (SIAM J. Numer. Anal., 2018)

A Spectral Penalty Method for Two-Sided Fractional Differential Equations with General Boundary Conditions. - Nan Wang 008; Zhiping Mao; Chengming Huang; George E. Karniadakis (SIAM J. Sci. Comput., 2019)

What is the fractional Laplacian? A comparative review with new results. - Anna Lischke; Guofei Pang; Mamikon A. Gulian; Fangying Song; Christian Glusa; Xiaoning Zheng; Zhiping Mao; Wei Cai 003; Mark M. Meerschaert; Mark Ainsworth; George Em Karniadakis (J. Comput. Phys., 2020)

Physics-informed neural networks (PINNs) for fluid mechanics: A review. - Shengze Cai; Zhiping Mao; Zhicheng Wang; Minglang Yin; George Em Karniadakis (CoRR, 2021)

DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators. - Zhiping Mao; Lu Lu 010; Olaf Marxen; Tamer A. Zaki; George Em Karniadakis (J. Comput. Phys., 2021)

DeepXDE: A Deep Learning Library for Solving Differential Equations. - Lu Lu 010; Xuhui Meng; Zhiping Mao; George Em Karniadakis (SIAM Rev., 2021)

Physics-informed neural networks for inverse problems in supersonic flows. - Ameya D. Jagtap; Zhiping Mao; Nikolaus A. Adams; George Em Karniadakis (J. Comput. Phys., 2022)

Learning functional priors and posteriors from data and physics. - Xuhui Meng; Liu Yang; Zhiping Mao; José del Águila Ferrandis; George Em Karniadakis (J. Comput. Phys., 2022)

A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition. - Yue Zhao; Zhiping Mao; Ling Guo; Yifa Tang; George Em Karniadakis (J. Comput. Phys., 2022)

Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving PDEs with sharp solutions. - Zhiping Mao; Xuhui Meng (CoRR, 2023)

Operator Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations Characterized by Sharp Solutions. - Bin Lin; Zhiping Mao; Zhicheng Wang; George Em Karniadakis (CoRR, 2023)

Analysis and Hermite Spectral Approximation of Diffusive-Viscous Wave Equations in Unbounded Domains Arising in Geophysics. - Dan Ling; Zhiping Mao (J. Sci. Comput., 2023)

DeepStSNet: Reconstructing the quantum state-resolved thermochemical nonequilibrium flowfield using deep neural operator learning with scarce data. - Jiaqi Lv; Qizhen Hong; Xiaoyong Wang; Zhiping Mao; Quanhua Sun (J. Comput. Phys., 2023)

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems. - Xiangnan Yu; Hao Xu; Zhiping Mao; HongGuang Sun; Yong Zhang; Dongxiao Zhang; Yuntian Chen (CoRR, 2024)

Efficient and stable SAV-based methods for gradient flows arising from deep learning. - Ziqi Ma; Zhiping Mao; Jie Shen 001 (J. Comput. Phys., 2024)

Physics-informed neural networks for supersonic flow over cones. - Zhen-tao Zhao; Wei Huang; Zhiping Mao; Chao-yang Liu; Yao-bin Niu (Comput. Phys. Commun., 2025)

Efficient and dissipation-preserving Hermite spectral Galerkin methods for diffusive-viscous wave equations in unbounded domains. - Dan Ling; Zhiping Mao (J. Comput. Appl. Math., 2025)

Deep collocation methods: A framework for solving PDEs using neural networks with error control. - Mingxing Weng; Zhiping Mao; Jie Shen (CoRR, 2025)

A novel class of arbitrary high-order numerical schemes for fractional differential equations. - Peng Ding; Zhiping Mao (CoRR, 2025)