SwitchNet: A Neural Network Model for Forward and Inverse Scattering Problems
Abstract
We propose a novel neural network architecture, SwitchNet, for solving wave equation based inverse scattering problems via providing maps between the scatterers and the scattered field (and vice versa). The main difficulty of using a neural network for this problem is that a scatterer has a global impact on the scattered wave field, rendering a typical convolutional neural network with local connections inapplicable. While it is possible to deal with such a problem using a fully connected network, the number of parameters grows quadratically with the size of the input and output data. By leveraging the inherent low-rank structure of the scattering problems and introducing a novel switching layer with sparse connections, the SwitchNet architecture uses far fewer parameters and facilitates the training process. Numerical experiments show promising accuracy in learning the forward and inverse maps between the scatterers and the scattered wave field.
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Information & Authors
Information
Published In
SIAM Journal on Scientific Computing
Pages: A3182 - A3201
DOI: 10.1137/18M1222399
ISSN (online): 1095-7197
Copyright
© 2019, Society for Industrial and Applied Mathematics.
History
Submitted: 23 October 2018
Accepted: 18 July 2019
Published online: 15 October 2019
Keywords
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Authors
Funding Information
Office of Science https://doi.org/10.13039/100006132
Funding Information
Google https://doi.org/10.13039/100006785
Funding Information
National Science Foundation https://doi.org/10.13039/100000001 : DMS-1818449
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