IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i1p150-d1559485.html
   My bibliography  Save this article

An Importance Sampling Method for Generating Optimal Interpolation Points in Training Physics-Informed Neural Networks

Author

Listed:
  • Hui Li

    (Department of Computer Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China)

  • Yichi Zhang

    (Department of Computer Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China)

  • Zhaoxiong Wu

    (Beijing Institute of Computer Technology and Applications, Beijing 100854, China)

  • Zhe Wang

    (Beijing Institute of Computer Technology and Applications, Beijing 100854, China)

  • Tong Wu

    (Beijing Institute of Computer Technology and Applications, Beijing 100854, China)

Abstract

The application of machine learning and artificial intelligence to solve scientific challenges has significantly increased in recent years. A remarkable development is the use of Physics-Informed Neural Networks (PINNs) to solve Partial Differential Equations (PDEs) numerically. However, current PINN techniques often face problems with accuracy and slow convergence. To address these problems, we propose an importance sampling method to generate optimal interpolation points during training. Experimental results demonstrate that our method achieves a 43% reduction in root mean square error compared to state-of-the-art methods when applied to the one-dimensional Korteweg–De Vries equation.

Suggested Citation

  • Hui Li & Yichi Zhang & Zhaoxiong Wu & Zhe Wang & Tong Wu, 2025. "An Importance Sampling Method for Generating Optimal Interpolation Points in Training Physics-Informed Neural Networks," Mathematics, MDPI, vol. 13(1), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:1:p:150-:d:1559485
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/1/150/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/1/150/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:13:y:2025:i:1:p:150-:d:1559485. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.