IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v230y2025icp80-93.html
   My bibliography  Save this article

Investigating neural networks with groundwater flow equation loss

Author

Listed:
  • Schiano Di Cola, Vincenzo
  • Bauduin, Vittorio
  • Berardi, Marco
  • Notarnicola, Filippo
  • Cuomo, Salvatore

Abstract

Physics-Informed Neural Networks (PINNs) are considered a powerful tool for solving partial differential equations (PDEs), particularly for the groundwater flow (GF) problem. In this paper, we investigate how the deep learning (DL) architecture, within the PINN framework, is connected to the ability to compute a more or less accurate numerical GF solution, so the link ‘PINN architecture - numerical performance’ is explored. Specifically, this paper explores the effect of various DL components, such as different activation functions and neural network structures, on the computational framework. Through numerical results and on the basis of some theoretical foundations of PINNs, this research aims to improve the explicability of PINNs to resolve, in this case, the one-dimensional GF equation. Moreover, our problem involves source terms described by a Dirac delta function, providing insights into the role of DL architecture in solving complex PDEs.

Suggested Citation

  • Schiano Di Cola, Vincenzo & Bauduin, Vittorio & Berardi, Marco & Notarnicola, Filippo & Cuomo, Salvatore, 2025. "Investigating neural networks with groundwater flow equation loss," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 230(C), pages 80-93.
    • Handle: RePEc:eee:matcom:v:230:y:2025:i:c:p:80-93
    DOI: 10.1016/j.matcom.2024.10.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424004373
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2024.10.039?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:eee:matcom:v:230:y:2025:i:c:p:80-93. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.