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The Inverse Scattering of Three-Dimensional Inhomogeneous Steady-State Sound Field Models

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  • Zhaoxi Sun

    (Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China)

  • Wenbin Zhang

    (Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China
    Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Baoding 071003, China)

  • Meiling Zhao

    (Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China
    Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Baoding 071003, China)

Abstract

We propose a U-Net regression network model for sliced data to reconstruct a three-dimensional irregular steady-state sound field filling inhomogeneous anisotropic media. Through an innovative sliced data processing strategy, the 3D reconstruction problem is decomposed into a combination of 2D problems, thereby significantly reducing the computational cost. The designed multi-channel U-Net fully utilizes the strengths of both the encoder and decoder, exhibiting strong feature extraction and spatial detail recovery capabilities. Numerical experiments show that the model can not only effectively reconstruct the complex sound field structure containing non-convex regions, but it can also synchronously restore the spatial distribution of the media and their parameter matrix, successfully achieving the dual reconstruction of the shape and physical parameters of the steady-state sound field.

Suggested Citation

  • Zhaoxi Sun & Wenbin Zhang & Meiling Zhao, 2025. "The Inverse Scattering of Three-Dimensional Inhomogeneous Steady-State Sound Field Models," Mathematics, MDPI, vol. 13(7), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1187-:d:1627860
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