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Deep Neural Network-Oriented Indicator Method for Inverse Scattering Problems Using Partial Data

Author

Listed:
  • Yule Lin

    (Department of Mathematics, Jinan University, Guangzhou 510632, China
    These authors contributed equally to this work.)

  • Xiaoyi Yan

    (Department of Mathematics, Jinan University, Guangzhou 510632, China
    These authors contributed equally to this work.)

  • Jiguang Sun

    (Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA
    These authors contributed equally to this work.)

  • Juan Liu

    (Department of Mathematics, Jinan University, Guangzhou 510632, China
    These authors contributed equally to this work.)

Abstract

We consider the inverse scattering problem to reconstruct an obstacle using partial far-field data due to one incident wave. A simple indicator function, which is negative inside the obstacle and positive outside of it, is constructed and then learned using a deep neural network (DNN). The method is easy to implement and effective as demonstrated by numerical examples. Rather than developing sophisticated network structures for the classical inverse operators, we reformulate the inverse problem as a suitable operator such that standard DNNs can learn it well. The idea of the DNN-oriented indicator method can be generalized to treat other partial data inverse problems.

Suggested Citation

  • Yule Lin & Xiaoyi Yan & Jiguang Sun & Juan Liu, 2024. "Deep Neural Network-Oriented Indicator Method for Inverse Scattering Problems Using Partial Data," Mathematics, MDPI, vol. 12(4), pages 1-8, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:522-:d:1335359
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    References listed on IDEAS

    as
    1. Li, Yixin & Hu, Xianliang, 2022. "Artificial neural network approximations of Cauchy inverse problem for linear PDEs," Applied Mathematics and Computation, Elsevier, vol. 414(C).
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