IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v31y2023i06ns0218348x23401035.html
   My bibliography  Save this article

Physics-Informed Neural Network For Solving Hausdorff Derivative Poisson Equations

Author

Listed:
  • GUOZHENG WU

    (College of Mechanical and Electrical Engineering, National Engineering Research Center for Intelligent Electrical, Vehicle Power System, Qingdao University, Qingdao 266071, P. R. China)

  • FAJIE WANG

    (College of Mechanical and Electrical Engineering, National Engineering Research Center for Intelligent Electrical, Vehicle Power System, Qingdao University, Qingdao 266071, P. R. China)

  • LIN QIU

    (College of Mechanical and Electrical Engineering, National Engineering Research Center for Intelligent Electrical, Vehicle Power System, Qingdao University, Qingdao 266071, P. R. China)

Abstract

This paper proposed a new physics-informed neural network (PINN) for solving the Hausdorff derivative Poisson equations (HDPEs) on irregular domains by using the concept of Hausdorff fractal derivative. The present scheme transforms the numerical solution of partial differential equation into an optimization problem including governing equation and boundary conditions. Like the meshless method, the developed PINN does not require grid generation and numerical integration. Moreover, it can freely address irregular domains and non-uniformly distributed nodes. The present study investigated different activation functions, and given an optimal choice in solving the HDPEs. Compared to other existing approaches, the PINN is simple, straightforward, and easy-to-program. Numerical experiments indicate that the new methodology is accurate and effective in solving the HDPEs on arbitrary domains, which provides a new idea for solving fractal differential equations.

Suggested Citation

  • Guozheng Wu & Fajie Wang & Lin Qiu, 2023. "Physics-Informed Neural Network For Solving Hausdorff Derivative Poisson Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(06), pages 1-15.
  • Handle: RePEc:wsi:fracta:v:31:y:2023:i:06:n:s0218348x23401035
    DOI: 10.1142/S0218348X23401035
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X23401035
    Download Restriction: Access to full text is restricted to subscribers

    File URL: https://libkey.io/10.1142/S0218348X23401035?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:fracta:v:31:y:2023:i:06:n:s0218348x23401035. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: https://www.worldscientific.com/worldscinet/fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.