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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
收藏
  |  
浏览/下载:10/0
  |  
提交时间:2023/02/07
Physics -informed neural networks
Fractional Laplacian
Nonlocal operators
Uncertainty quantification
The Fractional Tikhonov Regularization Method to Identify the Initial Value of the Nonhomogeneous Time-Fractional Diffusion Equation on a Columnar Symmetrical Domain
期刊论文
SYMMETRY-BASEL, 2022, 卷号: 14, 期号: 8
作者:
Chen, Yong-Gang
;
Yang, Fan
;
Li, Xiao-Xiao
;
Li, Dun-Gang
收藏
  |  
浏览/下载:26/0
  |  
提交时间:2022/09/22
time-fractional nonhomogeneous diffusion equation
columnar symmetric domain
ill-posed problem
fractional Tikhonov method
Fast Compact Difference Scheme for Solving the Two-Dimensional Time-Fractional Cattaneo Equation
期刊论文
FRACTAL AND FRACTIONAL, 2022, 卷号: 6, 期号: 8
作者:
Nong, Lijuan
;
Yi, Qian
;
Cao, Jianxiong
;
Chen, An
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  |  
浏览/下载:14/0
  |  
提交时间:2022/09/22
time-fractional Cattaneo equation
compact difference operator
L2-1(sigma) method
fast discrete Sine transform
sum of exponentials
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:9/0
  |  
提交时间:2023/02/07
Uncertainty quantification
Anomalous transport
Quasi Monte Carlo simulation
Generalized polynomial chaos
Long-time integration
Poly-fractonomials
Two Regularization Methods for Identifying the Source Term Problem on the Time-Fractional Diffusion Equation with a Hyper-Bessel Operator
期刊论文
ACTA MATHEMATICA SCIENTIA, 2022, 卷号: 42, 期号: 4, 页码: 1485-1518
作者:
Yang, Fan
;
Sun, Qiaoxi
;
Li, Xiaoxiao
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  |  
浏览/下载:8/0
  |  
提交时间:2022/07/19
Time-fractional diffusion equation
source term problem
fractional Landweber regularization method
Hyper-Bessel operator
fractional Tikhonov regularization method
Fractional Landweber Iterative Regularization Method for Identifying the Unknown Source of the Time-Fractional Diffusion Problem
期刊论文
ACTA APPLICANDAE MATHEMATICAE, 2021, 卷号: 175, 期号: 1
作者:
Yang, Fan
;
Fu, Jun-Liang
;
Fan, Ping
;
Li, Xiao-Xiao
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  |  
浏览/下载:3/0
  |  
提交时间:2021/12/17
Time-fractional diffusion equation
Ill-posed problem
Unknown source
Fractional Landweber iterative method
Three regularization methods for identifying the initial value of homogeneous anomalous secondary diffusion equation
期刊论文
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 卷号: 44, 期号: 17, 页码: 13723-13755
作者:
Yang, Fan
;
Wu, Hang-Hang
;
Li, Xiao-Xiao
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  |  
浏览/下载:3/0
  |  
提交时间:2021/10/14
homogeneous anomalous subdiffusion equation
identifying the initial value
inverse problem
optimal error bound
regularization method
The fractional Landweber method for identifying the space source term problem for time-space fractional diffusion equation
期刊论文
NUMERICAL ALGORITHMS, 2021, 卷号: 87, 期号: 3, 页码: 1229-1255
作者:
Yang, Fan
;
Pu, Qu
;
Li, Xiao-Xiao
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  |  
浏览/下载:6/0
  |  
提交时间:2021/10/14
Time-fractional diffusion equation
Fractional Laplacian
Identifying the unknown source
Fractional Landweber regularization
Ill-posed problem
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
Error estimates for a robust finite element method of two-term time-fractional diffusion-wave equation with nonsmooth data
期刊论文
MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2021, 卷号: 16
作者:
Nong, Lijuan
;
Chen, An
;
Cao, Jianxiong
收藏
  |  
浏览/下载:10/0
  |  
提交时间:2021/04/12
Two-term time-fractional diffusion-wave equation
finite element method
convolution quadrature
error estimate
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