Solving Inverse Scattering Problem with a Crack in Inhomogeneous Medium Based on a Convolutional Neural Network

Abstract

The direct and inverse scattering problems are a type of classical problem with symmetry. Numerical methods combined with machine learning are continuously being developed, and obtain good results in obstacle inversion problems. In this paper, we consider a crack shape with asymmetry; such problems are often ill-posed and nonlinear. Focusing on the inhomogeneous medium and limited-aperture far-field data, we propose a new sequence-to-sequence asymmetric convolutional neural network for recovering a crack via correlative far-field measurements. Taking the far-field data as the input and the shape parameters of a crack as the output, the features are quickly extracted using the convolutional and pooling layers. The Adam optimization algorithm is employed to update the weights and offsets of the neural network. Numerical experiments show that the proposed method can quickly and effectively reconstruct the shape of the crack.

On a Hybrid Method for Inverse Transmission Eigenvalue Problems

“…By a large number of training data, neural network can effectively learn the abstract relationship between model input and output, and reduce the impact of noise. Compared to the classical methods, neural network deals with the inverse problem from the perspective of data driven, which makes it possible for many more challenging problems [26,27,30]. In our neural network scheme, we first divide the wavenumber intervals into some subintervals based on prior information from the linear sampling method.…”