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Monte Carlo fPINNs: Deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations
期刊论文
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2022, 卷号: 400, 页码: 17
作者:
Guo, Ling
;
Wu, Hao
;
Yu, Xiaochen
;
Zhou, Tao
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  |  
浏览/下载:12/0
  |  
提交时间:2023/02/07
Physics -informed neural networks
Fractional Laplacian
Nonlocal operators
Uncertainty quantification
Optimal Holder continuity and hitting probabilities for SPDEs with rough fractional noises
期刊论文
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 卷号: 512, 期号: 1, 页码: 21
作者:
Hong, Jialin
;
Liu, Zhihui
;
Sheng, Derui
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  |  
浏览/下载:4/0
  |  
提交时间:2023/02/07
Stochastic partial differential equation
Fractional Brownian sheet
Hurst index H < 1/2
Holder exponent
Hitting probability
A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition
期刊论文
JOURNAL OF COMPUTATIONAL PHYSICS, 2022, 卷号: 461, 页码: 17
作者:
Zhao, Yue
;
Mao, Zhiping
;
Guo, Ling
;
Tang, Yifa
;
Karniadakis, George Em
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  |  
浏览/下载:11/0
  |  
提交时间:2023/02/07
Uncertainty quantification
Anomalous transport
Quasi Monte Carlo simulation
Generalized polynomial chaos
Long-time integration
Poly-fractonomials
Identifying initial value problem for time-fractional diffusion equation with Caputo-like counterpart hyper-Bessel operator: Optimal error bound analysis and regularization method
期刊论文
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 卷号: 44, 期号: 8, 页码: -
作者:
Yang, Fan
;
Sun, Qiao-Xi
;
Li, Xiao-Xiao
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  |  
浏览/下载:11/0
  |  
提交时间:2021/03/12
Errors
Initial value problems
Iterative methods
Numerical methods
Parameterization
Partial differential equations
Bessel operators
Error estimates
Exact solution
Iterative regularization
Optimal error bound
Regularization methods
Regularization parameters
Time fractional diffusion equation
A superlinear convergence scheme for the multi-term and distribution-order fractional wave equation with initial singularity
期刊论文
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2021, 页码: 16
作者:
Huang, Jianfei
;
Zhang, Jingna
;
Arshad, Sadia
;
Tang, Yifa
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浏览/下载:48/0
  |  
提交时间:2021/04/26
distribution-order derivative
fractional wave equations
initial singularity
multi-term fractional derivatives
superlinear convergence
The fractional Tikhonov regularization methods for identifying the initial value problem for a time-fractional diffusion equation
期刊论文
Journal of Computational and Applied Mathematics, 2020, 卷号: 380
作者:
Yang, Fan
;
Pu, Qu
;
Li, Xiao-Xiao
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  |  
浏览/下载:10/0
  |  
提交时间:2022/02/17
Initial value problems
Parameterization
Partial differential equations
Columnar axis
Error estimates
Exact solution
Regularization parameters
Symmetric domains
Tikhonov method
Tikhonov regularization method
Time fractional diffusion equation
Error estimate on the tanh meshes for the time fractional diffusion equation
期刊论文
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2020, 页码: 21
作者:
Zhang, Jiali
;
Huang, Jizu
;
Wang, Kun
;
Wang, Xin
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浏览/下载:9/0
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提交时间:2021/01/14
Caputo fractional derivative
error estimate
the tanh meshes
unconditionally stable
weak singularity
Review and new theoretical perspectives on active disturbance rejection control for uncertain finite-dimensional and infinite-dimensional systems
期刊论文
NONLINEAR DYNAMICS, 2020, 页码: 25
作者:
Wu, Ze-Hao
;
Zhou, Hua-Cheng
;
Guo, Bao-Zhu
;
Deng, Feiqi
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浏览/下载:17/0
  |  
提交时间:2020/09/23
Active disturbance rejection control
Extended state observer
Boundary control
Disturbance
Stochastic systems
Infinite-dimensional systems
Fractional-order PDE
A limited-memory block bi-diagonal Toeplitz preconditioner for block lower triangular Toeplitz system from time–space fractional diffusion equation
期刊论文
Journal of Computational and Applied Mathematics, 2019, 卷号: 362, 页码: 99-115
作者:
Zhao, Yong-Liang
;
Zhu, Pei-Yong
;
Gu, Xian-Ming
;
Zhao, Xi-Le
;
Cao, Jianxiong
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  |  
浏览/下载:5/0
  |  
提交时间:2020/11/14
Gradient methods
Linear systems
Matrix algebra
Partial differential equations
Circulant preconditioner
Fractional differential equations
Krylov subspace method
Toeplitz matrices
WSGD
Mittag-Leffler stabilization for an unstable time-fractional anomalous diffusion equation with boundary control matched disturbance
期刊论文
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2019, 卷号: 29, 期号: 13, 页码: 4384-4401
作者:
Zhou, Hua-Cheng
;
Lv, Chunwan
;
Guo, Bao-Zhu
;
Chen, YangQuan
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  |  
浏览/下载:60/0
  |  
提交时间:2020/01/10
active disturbance rejection control (ADRC)
Mittag-Leffler stabilization
time-fractional anomalous diffusion equation
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