IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i8p1190-d1376575.html
   My bibliography  Save this article

Modeling Error and Nonuniqueness of the Continuous-Time Models Learned via Runge–Kutta Methods

Author

Listed:
  • Shunpei Terakawa

    (Department of Computational Science, Graduate School of System Informatics, Kobe University, Kobe 657-8501, Japan)

  • Takaharu Yaguchi

    (Department of Mathematics, Graduate School of Science, Kobe University, Kobe 657-8501, Japan)

Abstract

In the present study, we consider continuous-time modeling of dynamics using observed data and formulate the modeling error caused by the discretization method used in the process. In the formulation, a class of linearized dynamics called Dahlquist’s test equations is used as representative of the target dynamics, and the characteristics of each discretization method for various dynamics are taken into account. The family of explicit Runge–Kutta methods is analyzed as a specific discretization method using the proposed framework. As a result, equations for predicting the modeling error are derived, and it is found that there can be multiple possible models obtained when using these methods. Several learning experiments using a simple neural network exhibited consistent results with theoretical predictions, including the nonuniqueness of the resulting model.

Suggested Citation

  • Shunpei Terakawa & Takaharu Yaguchi, 2024. "Modeling Error and Nonuniqueness of the Continuous-Time Models Learned via Runge–Kutta Methods," Mathematics, MDPI, vol. 12(8), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1190-:d:1376575
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/8/1190/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/8/1190/
    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:12:y:2024:i:8:p:1190-:d:1376575. 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.