毛志平｜厦门大学｜学者主页

2026

Operator learning augmented physics-informed neural networks for partial differential equations exhibiting sharp features

Bin Lin, Zhiping Mao, Zhicheng Wang

Physical review. E

DOI

2025

Efficient and dissipation-preserving Hermite spectral Galerkin methods for diffusive-viscous wave equations in unbounded domains

Dan Ling, Zhiping Mao

Journal of Computational and Applied Mathematics

DOI

2025

Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation

Zhang-Yong Liang, Zhiping Mao, Xiaofei Zhao

arXiv.org

DOI

2025

Deep Collocation Method: A Framework for Solving PDEs Using Neural Networks with Error Control

Mingxing Weng, Zhiping Mao, Jie Shen

SIAM Journal on Scientific Computing

DOI

2024

深度学习在科学计算与工程中的应用与探索

毛志平

《人工智能》

2024

一类结合神经算子网络与贝叶斯神经网络的主动学习算法：从微观数据学习集群行为的宏观模型

高正雅，毛志平

《计算物理》

2024

Efficient and stable SAV-based methods for gradient flows arising from deep learning

Zi-Qi Ma, Zhiping Mao, Jie Shen

Journal of Computational Physics

DOI

2024

A data-driven framework for discovering fractional differential equations in complex systems

Xiang-Nan Yu, Hao Xu, Zhiping Mao, Hong-Guang Sun, Yong Zhang, Zhi-Bo Chen, Dong-Xiao Zhang, Yun-Tian Chen

Nonlinear dynamics

DOI

2023

非线性偏微分方程高效算法研究

陈黄鑫，毛志平，许传炬

《厦门大学学报(自然科学版)》

2023

Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving partial differential equations with sharp solutions

Zhiping Mao, Xuhui Meng

Applied Mathematics and Mechanics

DOI

2023

Operator Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations Characterized by Sharp Solutions

Bin Lin, Zhiping Mao, Zhi-Cheng Wang, G. Karniadakis

arXiv.org

DOI

2023

High Order Conservative Finite Difference/Fourier Spectral Methods for Inviscid Surface Quasi-Geostrophic Flows

Nan Zhang, Zhiping Mao, Tao Xiong

Communications in Computational Physics

DOI

2022

Analysis and Hermite Spectral Approximation of Diffusive-Viscous Wave Equations in Unbounded Domains Arising in Geophysics

Dan Ling, Zhiping Mao

Journal of Scientific Computing

DOI

2022

A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition

Yue Zhao, Zhiping Mao, Ling Guo, Yi-Fa Tang, G. Karniadakis

Journal of Computational Physics

DOI

2022

Efficient and Accurate Numerical Methods Using the Accelerated Spectral Deferred Correction for Solving Fractional Differential Equations

Xuejuan Chen, Zhiping Mao, George Em Karniadakis

Numerical Mathematics Theory Methods and Applications

DOI

2021

Learning Functional Priors and Posteriors from Data and Physics

Xuhui Meng, Liu Yang, Zhiping Mao, J. del Águila Ferrandis, G. Karniadakis

Journal of Computational Physics

DOI

2021

Physics-informed neural networks (PINNs) for fluid mechanics: a review

Sheng-Ze Cai, Zhiping Mao, Zhi-Cheng Wang, Minglang Yin, G. Karniadakis

Acta Mechanica Sinica

DOI

2021

A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data

Lu Lu, Xuhui Meng, Sheng-Ze Cai, Zhiping Mao, S. Goswami, Zhongqiang Zhang, G. Karniadakis

Computer Methods in Applied Mechanics and Engineering

DOI

2020

Fractional calculus and numerical methods for fractional PDEs

Ehsan Kharazmi, Zhiping Mao, G. Pang, Mohsen Zayernouri, G. Karniadakis

DOI

2020

A fast solver for spectral elements applied to fractional differential equations using hierarchical matrix approximation

Xian-Juan Li, Zhiping Mao, Nan Wang, Fangying Song, Hong Wang, G. Karniadakis

DOI

2020

Fractional phase-field crystal modelling: analysis, approximation and pattern formation

M. Ainsworth, Zhiping Mao

DOI

2019

Analysis and Approximation of Gradient Flows Associated with a Fractional Order Gross–Pitaevskii Free Energy

M. Ainsworth, Zhiping Mao

Communication on Applied Mathematics and Computation

DOI

2019

Phase field crystal based prediction of temperature and density dependence of elastic constants through a structural phase transition

M. Ainsworth, Zhiping Mao

Physical review B

DOI

2019

DeepXDE: A Deep Learning Library for Solving Differential Equations

Lu Lu, Xuhui Meng, Zhiping Mao, G. Karniadakis

AAAI Spring Symposium: MLPS

DOI

2018

Multi-domain spectral collocation method for variable-order nonlinear fractional differential equations

Ting-Gang Zhao, Zhiping Mao, G. Karniadakis

Computer Methods in Applied Mechanics and Engineering

DOI

2018

A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative

Zhiping Mao, G. Karniadakis

SIAM Journal on Numerical Analysis

DOI

2018

What is the fractional Laplacian? A comparative review with new results

Anna Lischke, G. Pang, Mamikon A. Gulian, Fangying Song, Christian Glusa, Xiaoning Zheng, Zhiping Mao, W. Cai, M. Meerschaert, M. Ainsworth, G. Karniadakis

Journal of Computational Physics

DOI

2018

Nonlocal Flocking Dynamics: Learning the Fractional Order of PDEs from Particle Simulations

Zhiping Mao, Zhen Li, G. Karniadakis

Communication on Applied Mathematics and Computation

DOI

2018

A Spectral Penalty Method for Two-Sided Fractional Differential Equations with General Boundary Conditions

Nan Wang, Zhiping Mao, Cheng-Ming Huang, G. Karniadakis

SIAM Journal on Scientific Computing

DOI

2017

Analysis and Approximation of a Fractional Cahn-Hilliard Equation

M. Ainsworth, Zhiping Mao

SIAM Journal on Numerical Analysis

DOI

2017

Fractional Burgers equation with nonlinear non-locality: Spectral vanishing viscosity and local discontinuous Galerkin methods

Zhiping Mao, G. Karniadakis

Journal of Computational Physics

DOI

2017

Spectral element method with geometric mesh for two-sided fractional differential equations

Zhiping Mao, Jie Shen

Advances in Computational Mathematics

DOI

2017

Well-posedness of the Cahn–Hilliard equation with fractional free energy and its Fourier Galerkin approximation

M. Ainsworth, Zhiping Mao

DOI

2017

A Generalized Spectral Collocation Method with Tunable Accuracy for Fractional Differential Equations with End-Point Singularities

Fanhai Zeng, Zhiping Mao, G. Karniadakis

SIAM Journal on Scientific Computing

DOI

2017

Hermite Spectral Methods for Fractional PDEs in Unbounded Domains

Zhiping Mao, Jie Shen

SIAM Journal on Scientific Computing

DOI

2016

Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients

Zhiping Mao, Jie Shen

Journal of Computational Physics

DOI

2016

Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations

Zhiping Mao, Sheng Chen, Jie Shen

DOI

2015

A semi-implicit spectral deferred correction method for two water wave models with nonlocal viscous term and numerical study of their decay rates

Zhiping Mao, Jie Shen

DOI

精选作品

期刊论文

Operator learning augmented physics-informed neural networks for partial differential equations exhibiting sharp features

Efficient and dissipation-preserving Hermite spectral Galerkin methods for diffusive-viscous wave equations in unbounded domains

Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation

Deep Collocation Method: A Framework for Solving PDEs Using Neural Networks with Error Control

深度学习在科学计算与工程中的应用与探索

一类结合神经算子网络与贝叶斯神经网络的主动学习算法：从微观数据学习集群行为的宏观模型

Efficient and stable SAV-based methods for gradient flows arising from deep learning

A data-driven framework for discovering fractional differential equations in complex systems

非线性偏微分方程高效算法研究

Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving partial differential equations with sharp solutions

Operator Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations Characterized by Sharp Solutions

High Order Conservative Finite Difference/Fourier Spectral Methods for Inviscid Surface Quasi-Geostrophic Flows

Analysis and Hermite Spectral Approximation of Diffusive-Viscous Wave Equations in Unbounded Domains Arising in Geophysics

A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition

Efficient and Accurate Numerical Methods Using the Accelerated Spectral Deferred Correction for Solving Fractional Differential Equations

Learning Functional Priors and Posteriors from Data and Physics

Physics-informed neural networks (PINNs) for fluid mechanics: a review

A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data

Fractional calculus and numerical methods for fractional PDEs

A fast solver for spectral elements applied to fractional differential equations using hierarchical matrix approximation

Fractional phase-field crystal modelling: analysis, approximation and pattern formation

Analysis and Approximation of Gradient Flows Associated with a Fractional Order Gross–Pitaevskii Free Energy

Phase field crystal based prediction of temperature and density dependence of elastic constants through a structural phase transition

DeepXDE: A Deep Learning Library for Solving Differential Equations

Multi-domain spectral collocation method for variable-order nonlinear fractional differential equations

A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative

What is the fractional Laplacian? A comparative review with new results

Nonlocal Flocking Dynamics: Learning the Fractional Order of PDEs from Particle Simulations

A Spectral Penalty Method for Two-Sided Fractional Differential Equations with General Boundary Conditions

Analysis and Approximation of a Fractional Cahn-Hilliard Equation

Fractional Burgers equation with nonlinear non-locality: Spectral vanishing viscosity and local discontinuous Galerkin methods

Spectral element method with geometric mesh for two-sided fractional differential equations

Well-posedness of the Cahn–Hilliard equation with fractional free energy and its Fourier Galerkin approximation

A Generalized Spectral Collocation Method with Tunable Accuracy for Fractional Differential Equations with End-Point Singularities

Hermite Spectral Methods for Fractional PDEs in Unbounded Domains

Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients

Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations

A semi-implicit spectral deferred correction method for two water wave models with nonlocal viscous term and numerical study of their decay rates

预印本

Multi-stage neural operator learning with application for convolutions

Memory-Augmented Phase-Field Modeling: Onsager Formulation, Internal-Variable Lifting, and Structure-Preserving Computation

Several Accelerated and Stable Pseudo-Energy-Dissipative Lagrange Multiplier Methods based on Second-order Flow and Variable Splitting

ViT-K: A Few-Shot Learning Model for Coupled Fluid-Porous Media Flows with Interface Conditions

A novel class of arbitrary high-order numerical schemes for fractional differential equations

Jacobi-Galerkin spectral method for eigenvalue problems of Riesz fractional differential equations

研究方向