Methods and Algorithms for Scientific Computing

SwitchNet: A Neural Network Model for Forward and Inverse Scattering Problems


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.


  1. Helmholtz equation
  2. inverse problem
  3. artificial neural network
  4. operator compression

MSC codes

  1. 65R10
  2. 65T50

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Information & Authors


Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: A3182 - A3201
ISSN (online): 1095-7197


Submitted: 23 October 2018
Accepted: 18 July 2019
Published online: 15 October 2019


  1. Helmholtz equation
  2. inverse problem
  3. artificial neural network
  4. operator compression

MSC codes

  1. 65R10
  2. 65T50



Funding Information

Office of Science

Funding Information


Funding Information

National Science Foundation : DMS-1818449

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