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

Yule Lin, Xiaoyi Yan, Jiguang Sun and Juan Liu ()
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Yule Lin: Department of Mathematics, Jinan University, Guangzhou 510632, China
Xiaoyi Yan: Department of Mathematics, Jinan University, Guangzhou 510632, China
Jiguang Sun: Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA
Juan Liu: Department of Mathematics, Jinan University, Guangzhou 510632, China

Mathematics, 2024, vol. 12, issue 4, 1-8

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.

Keywords: inverse obstacle scattering; deep neural network; partial data; indicator function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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