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

Dazhi Zhao, Guozhu Yu and Weibin Li ()
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Dazhi Zhao: School of Sciences, Southwest Petroleum University, Chengdu 610500, P. R. China†Institute for Artificial Intelligence, Southwest Petroleum University, Chengdu 610500, P. R. China
Guozhu Yu: ��School of Mathematics, Southwest Jiaotong University, Chengdu 610031, P. R. China
Weibin Li: �China Aerodynamics Research and Development Center, Mianyang 621000, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 03, 1-12

Abstract: 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.

Keywords: Fractal; Conformable Fractional Derivative; Fractal Derivative; Physics-Informed Neural Network (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500717

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