New semi-analytical solutions of the time-fractional Fokker-Planck equation by the neural network method

被引：11
|
作者：
Wei, Jia-Li [1 ,2 ]
Wu, Guo-Cheng [2 ]
Liu, Bao-Qing [1 ]
Zhao, Zhengang [3 ]
机构：
[1] Nanjing Univ Finance & Econ, Sch Appl Math, Nanjing 210023, Jiangsu, Peoples R China
[2] Neijiang Normal Univ, Coll Math & Informat Sci, Data Recovery Key Lab Sichuan Prov, Neijiang 641100, Peoples R China
[3] Shanghai Customs Coll, Dept Fundamental Courses, Shanghai 201204, Peoples R China
来源：
OPTIK | 2022年 / 259卷
基金：
中国国家自然科学基金; 上海市自然科学基金;
关键词：
Fractional Fokker-Planck equation; L-1 numerical scheme; Neural network; Gradient descent algorithm; DIFFERENTIAL-EQUATIONS; APPROXIMATE; DIFFUSION;
D O I：
10.1016/j.ijleo.2022.168896
中图分类号：
O43 [光学];
学科分类号：
070207 ; 0803 ;
摘要：
This paper suggests a neural network method for solving the time-fractional Fokker-Planck equation. An energy function is constructed by means of initial-boundary value conditions. The Caputo derivative is approximated by L-1 numerical scheme and an unconstrained discretization minimization problem is presented. Gradient descent algorithm is adopted for neural network training. Semi-analytical solutions are obtained where two numerical examples demonstrate the method's efficiency.
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页数：10
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