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

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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.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Puducherry, Karaikal, 609609, India

    Sivalingam S M & V. Govindaraj

  2. Institute for the Future of Knowledge, University of Johannesburg, PO Box 524, Auckland Park 2006, Johannesburg, South Africa

    Pushpendra Kumar

Authors
  1. Sivalingam S M
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  2. Pushpendra Kumar
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  3. V. Govindaraj
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Contributions

SMS:  conceptualization, visualization, software, resources, formal analysis, investigation, writing—original draft. PK:  conceptualization, investigation, resources, visualization, writing—review and editing. VG: supervision, formal analysis, writing—review and editing.

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Correspondence to Pushpendra Kumar.

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S M, S., Kumar, P. & Govindaraj, V. A novel optimization-based physics-informed neural network scheme for solving fractional differential equations. Engineering with Computers 40, 855–865 (2024). https://doi.org/10.1007/s00366-023-01830-x

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