IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i5p725-d1598268.html
   My bibliography  Save this article

Solving Inverse Wave Problems Using Spacetime Radial Basis Functions in Neural Networks

Author

Listed:
  • Chih-Yu Liu

    (Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan
    Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan)

  • Cheng-Yu Ku

    (Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan
    Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan)

  • Wei-Da Chen

    (Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan)

  • Ying-Fan Lin

    (Department of Civil Engineering, Chung Yuan Christian University, Taoyuan 320314, Taiwan)

  • Jun-Hong Lin

    (Department of Civil Engineering, Chung Yuan Christian University, Taoyuan 320314, Taiwan)

Abstract

Conventional methods for solving inverse wave problems struggle with ill-posedness, significant computational demands, and discretization errors. In this study, we propose an innovative framework for solving inverse problems in wave equations by using deep learning techniques with spacetime radial basis functions (RBFs). The proposed method capitalizes on the pattern recognition strength of deep neural networks (DNNs) and the precision of spacetime RBFs in capturing spatiotemporal dynamics. By utilizing initial conditions, boundary data, and radial distances to construct spacetime RBFs, this approach circumvents the need for wave equation discretization. Notably, the model maintains accuracy even with incomplete or noisy boundary data, illustrating its robustness and offering significant advancements over traditional techniques in solving wave equations.

Suggested Citation

  • Chih-Yu Liu & Cheng-Yu Ku & Wei-Da Chen & Ying-Fan Lin & Jun-Hong Lin, 2025. "Solving Inverse Wave Problems Using Spacetime Radial Basis Functions in Neural Networks," Mathematics, MDPI, vol. 13(5), pages 1-21, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:725-:d:1598268
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/5/725/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/5/725/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hrvoje Dodig, 2024. "The Wave Equation for a Moving Source and a Moving Receiver," Mathematics, MDPI, vol. 12(14), pages 1-17, July.
    2. Chih-Yu Liu & Cheng-Yu Ku & Wei-Da Chen, 2024. "A Spacetime RBF-Based DNNs for Solving Unsaturated Flow Problems," Mathematics, MDPI, vol. 12(18), pages 1-25, September.
    3. Chih-Yu Liu & Cheng-Yu Ku, 2023. "A Novel ANN-Based Radial Basis Function Collocation Method for Solving Elliptic Boundary Value Problems," Mathematics, MDPI, vol. 11(18), pages 1-19, September.
    4. Imre Ferenc Barna & Mihály András Pocsai & László Mátyás, 2022. "Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths," Mathematics, MDPI, vol. 10(13), pages 1-16, July.
    5. Zhang, Fan & Li, Po-Wei & Gu, Yan & Fan, Chia-Ming, 2025. "A space-time generalized finite difference scheme for long wave propagation based on high-order Korteweg-de Vries type equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 298-312.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dmitry Stenkin & Vladimir Gorbachenko, 2024. "Mathematical Modeling on a Physics-Informed Radial Basis Function Network," Mathematics, MDPI, vol. 12(2), pages 1-11, January.
    2. Chih-Yu Liu & Cheng-Yu Ku & Wei-Da Chen, 2024. "A Spacetime RBF-Based DNNs for Solving Unsaturated Flow Problems," Mathematics, MDPI, vol. 12(18), pages 1-25, September.

    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:5:p:725-:d:1598268. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.