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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:7/0
  |  
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:3/0
  |  
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
收藏
  |  
浏览/下载:8/0
  |  
提交时间:2023/02/07
Uncertainty quantification
Anomalous transport
Quasi Monte Carlo simulation
Generalized polynomial chaos
Long-time integration
Poly-fractonomials
A fast Euler-Maruyama method for fractional stochastic differential equations
期刊论文
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2022, 页码: 19
作者:
Zhang, Jingna
;
Tang, Yifa
;
Huang, Jianfei
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  |  
浏览/下载:1/0
  |  
提交时间:2023/02/07
Fractional stochastic differential equations
Euler-Maruyama method
Sum-of-exponentials approximation
Strong convergence
Computational efficiency
Transport properties of mixed convective nano-material flow considering the generalized fourier law and a vertical surface: Concept of caputo-time fractional derivative
期刊论文
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART A-JOURNAL OF POWER AND ENERGY, 2022, 页码: 11
作者:
Raza, Ali
;
Khan, Sami Ullah
;
Farid, Saadia
;
Khan, Muhammad Ijaz
;
Khan, M. Riaz
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  |  
浏览/下载:5/0
  |  
提交时间:2023/02/07
Newtonian
slip
convective flow
fourier's law
fractional derivatives
Simpson's method for fractional differential equations with a non-singular kernel applied to a chaotic tumor model
期刊论文
PHYSICA SCRIPTA, 2021, 卷号: 96, 期号: 12, 页码: 19
作者:
Arshad, Sadia
;
Saleem, Iram
;
Defterli, Ozlem
;
Tang, Yifa
;
Baleanu, Dumitru
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  |  
浏览/下载:3/0
  |  
提交时间:2022/04/02
fractional operator with the non-singular kernel
numerical approximation
stability analysis
convergence analysis
tumor model
chaos
Simpson’s method for fractional differential equations with a non-singular kernel applied to a chaotic tumor model
期刊论文
Physica Scripta, 2021, 卷号: 96, 期号: 12
作者:
Arshad,Sadia
;
Saleem,Iram
;
Defterli,Ozlem
;
Tang,Yifa
;
Baleanu,Dumitru
收藏
  |  
浏览/下载:5/0
  |  
提交时间:2022/04/02
fractional operator with the non-singular kernel
numerical approximation
stability analysis
convergence analysis
tumor model
chaos
Numerical Schemes for Time-Space Fractional Vibration Equations
期刊论文
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2021, 卷号: 13, 期号: 4, 页码: 806-826
作者:
Zhang, Jingna
;
Aleroev, Temirkhan S.
;
Tang, Yifa
;
Huang, Jianfei
收藏
  |  
浏览/下载:82/0
  |  
提交时间:2021/06/01
Time-space fractional vibration equations
ADI scheme
stability
convergence
Optimal rate of convergence for two classes of schemes to stochastic differential equations driven by fractional Brownian motions
期刊论文
IMA JOURNAL OF NUMERICAL ANALYSIS, 2021, 卷号: 41, 期号: 2, 页码: 1608-1638
作者:
Hong, Jialin
;
Huang, Chuying
;
Wang, Xu
收藏
  |  
浏览/下载:7/0
  |  
提交时间:2021/10/26
fractional Brownian motion
strong convergence rate
Runge-Kutta method
simplified step-N Euler scheme
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
期刊论文
NATURE MACHINE INTELLIGENCE, 2021, 卷号: 3, 期号: 3, 页码: 218-+
作者:
Lu, Lu
;
Jin, Pengzhan
;
Pang, Guofei
;
Zhang, Zhongqiang
;
Karniadakis, George Em
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  |  
浏览/下载:76/0
  |  
提交时间:2021/06/01
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