# SwitchNet: a neural network model for forward and inverse scattering problems

arXiv: https://arxiv.org/abs/1810.09675 · HTML: https://mlsanity.com/paper/1810.09675/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2018.

## Built on by (most cited first, 30 of 35)

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- [Multigrid-Augmented Deep Learning Preconditioners for the Helmholtz Equation using Compact Implicit Layers](https://mlsanity.com/paper/2306.17486/) (2023)
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- [Reinforced Inverse Scattering](https://mlsanity.com/paper/2206.04186/) (2022)
- [Operator learning for hyperbolic partial differential equations](https://mlsanity.com/paper/2312.17489/) (2023)
- [VI-DGP: A variational inference method with deep generative prior for solving high-dimensional inverse problems](https://mlsanity.com/paper/2302.11173/) (2023)
- [A Direct Sampling-Based Deep Learning Approach for Inverse Medium Scattering Problems](https://mlsanity.com/paper/2305.00250/) (2023)
- [Accurate and Robust Deep Learning Framework for Solving Wave-Based Inverse Problems in the Super-Resolution Regime](https://mlsanity.com/paper/2106.01143/) (2021)
- [Deep Injective Prior for Inverse Scattering](https://mlsanity.com/paper/2301.03092/) (2023)
- [Back-Projection Diffusion: Solving the Wideband Inverse Scattering Problem with Diffusion Models](https://mlsanity.com/paper/2408.02866/) (2024)
- [Self-composing neural operators for high-frequency and multiscale PDE surrogates](https://mlsanity.com/paper/2508.20650/) (2025)
- [Conductivity Imaging from Internal Measurements with Mixed Least-Squares Deep Neural Networks](https://mlsanity.com/paper/2303.16454/) (2023)
- [Solving the Wide-band Inverse Scattering Problem via Equivariant Neural Networks](https://mlsanity.com/paper/2212.06068/) (2022)
- [Physics-aware deep learning framework for the limited aperture inverse obstacle scattering problem](https://mlsanity.com/paper/2403.19470/) (2024)
- [Practical Aspects on Solving Differential Equations Using Deep Learning: A Primer](https://mlsanity.com/paper/2408.11266/) (2024)
- [Neumann Series-based Neural Operator for Solving Inverse Medium Problem](https://mlsanity.com/paper/2409.09480/) (2024)
- [A physics informed neural network approach to simulating ice dynamics governed by the shallow ice approximation](https://mlsanity.com/paper/2504.08136/) (2025)
- [Deep Micro Solvers for Rough-Wall Stokes Flow in a Heterogeneous Multiscale Method](https://mlsanity.com/paper/2507.13902/) (2025)

## Abstract (arXiv)

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.