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

Abstract

We propose a novel neural network architecture, SwitchNet, for solving the 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 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 much 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.

Artificial neural networks for nonlinear pulse shaping in optical fibers

“…An interesting extension of the method described will be to the analysis of the attraction of parabolic pulses towards a selfsimilar state in normally dispersive nonlinear fibers with linear gain [4]. Furthermore, although demonstrated here in a fiber optics context, the principle of using NN architectures to solve wave equation-based inverse problems is expected to apply to many physical systems [30,31].…”

Solving electrical impedance tomography with deep learning

“…A second main direction focuses on the low-dimensional parameterized PDE problems, by using the DNNs to represent the nonlinear map from the high-dimensional parameters of the PDE solution [52,36,43,25,24,23,51,7]. Applying DNNs to inverse problems [45,40,41,2,53,61,26,56] can be viewed as a particularly important case of this direction. This paper applies the deep learning approach to the two-dimensional OT problems by representing both the forward and inverse maps using neural network architectures.…”

A Review of Deep Learning Approaches for Inverse Scattering Problems (Invited Review)

“…Physical knowledge and its mathematical properties can also be exploited to design desirable architecture of NNs. In [31], the NN still provides a map between the scatterers and the scattered field, but it introduces a novel switching layer with sparse connections. The new NN architecture, named the SwitchNet, uses far fewer parameters and facilitates the training process.…”

“…The paper carefully analyzes the inherent low-rank structure of the scattering problems, which motivates the introduction of a novel switching layer with sparse connections. It is pointed in [31] that if a NN still provides a map between the scatterers and the scattered field, then a typical CNN with local connections is usually inapplicable since a scatterer has a global impact on the scattered wave field.…”