DIFFUSION ON FRACTAL OBJECTS MODELING AND ITS PHYSICS-INFORMED NEURAL NETWORK SOLUTION

被引：6

作者：

Zhao, Dazhi ^{[1
,2
]}

Yu, Guozhu ^{[3
]}

Li, Weibin ^{[4
]}

机构：

[1] Southwest Petr Univ, Sch Sci, Chengdu 610500, Peoples R China

[2] Southwest Petr Univ, Inst Artificial Intelligence, Chengdu 610500, Peoples R China

[3] Southwest Jiaotong Univ, Sch Math, Chengdu 610031, Peoples R China

[4] China Aerodynam Res & Dev Ctr, Mianyang 621000, Sichuan, Peoples R China

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2021年 / 29卷 / 03期

关键词：

Fractal; Conformable Fractional Derivative; Fractal Derivative; Physics-Informed Neural Network; ANOMALOUS DIFFUSION; FRAMEWORK; MECHANICS; CALCULUS; EQUATION;

D O I：

10.1142/S0218348X21500717

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Fractional operators are the main tools to describe diffusion problems on fractal objects. This paper first shows the equivalence between conformable fractional derivative and fractal derivative, and then investigates various models for the diffusion on fractal objects by the conformable fractional derivative and its generalized form. The recommended models are solved by the mesh-free physics-informed neural network method with high computational effectiveness and universality.

引用

页数：12

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