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

Author

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  • 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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Hrvoje Dodig, 2024. "The Wave Equation for a Moving Source and a Moving Receiver," Mathematics, MDPI, vol. 12(14), pages 1-17, July.
    Full references (including those not matched with items on IDEAS)

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