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

Chih-Yu Liu, Cheng-Yu Ku (), Wei-Da Chen, Ying-Fan Lin and Jun-Hong Lin
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Chih-Yu Liu: Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan
Cheng-Yu Ku: Department of Harbor and River 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

Mathematics, 2025, vol. 13, issue 5, 1-21

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.

Keywords: inverse problems; wave equations; deep learning; physics-informed neural networks; radial basis functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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