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Engineering with Computers
Erschienen in: Engineering with Computers 2/2024

08.05.2023 | Original Article

A novel optimization-based physics-informed neural network scheme for solving fractional differential equations

verfasst von: Sivalingam S M, Pushpendra Kumar, V. Govindaraj

Erschienen in: Engineering with Computers | Ausgabe 2/2024

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Abstract

Nowadays, the study of neural networks is one of the most interesting research topics. In this article, we introduce a novel scheme based on Physics Informed Neural Network (PINN) for solving Fractional Differential Equations (FDEs) in terms of Caputo derivative. We use a trial solution based on the Theory of Functional Connection called the constrained expression to obtain the approximate solution. The training is proposed using the recently introduced average and subtraction-based optimizer algorithm. We implement the proposed algorithm to obtain the approximate solutions of single as well as a system of FDEs. The proposed scheme eliminates the primary drawbacks of the standard PINN. With our scheme, we overcome the choice of additional parameters that affect the convergence.
Vorheriger Artikel GAS-AU: an average uncertainty-based general adaptive sampling approach
Nächster Artikel Memory-efficient boundary-preserving tetrahedralization of large three-dimensional meshes

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Metadaten
Titel
A novel optimization-based physics-informed neural network scheme for solving fractional differential equations
verfasst von
Sivalingam S M
Pushpendra Kumar
V. Govindaraj
Publikationsdatum
08.05.2023
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 2/2024
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-023-01830-x

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