mlsanityData to 7 Oct 2026

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

arXiv 1810.09675 ↗First posted 23 Oct 2018math.NA cs.LG cs.NAcited by 35

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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.

Key facts. Cited by 35 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Oct 2018.

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Citing papers per year: 2021: 3; 2022: 9; 2023: 8; 2024: 6; 2025: 6; 2026: 3.

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  6. 2022Multigrid-augmented deep learning preconditioners for the Helmholtz equationcited by 24
  7. 2023Deep Operator Learning Lessens the Curse of Dimensionality for PDEscited by 18
  8. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  9. 2022IAE-Net: Integral Autoencoders for Discretization-Invariant Learningcited by 15
  10. 2022Multiscale Neural Operator: Learning Fast and Grid-independent PDE Solverscited by 12
  11. 2024Generalization Error Guaranteed Auto-Encoder-Based Nonlinear Model Reduction for Operator Learningcited by 12
  12. 2023Multigrid-Augmented Deep Learning Preconditioners for the Helmholtz Equation using Compact Implicit Layerscited by 11
23 more
  1. 2022A Neural Network Warm-Start Approach for the Inverse Acoustic Obstacle Scattering Problemcited by 8
  2. 2024Nonlinear functional regression by functional deep neural network with kernel embeddingcited by 7
  3. 2022Imaging Conductivity from Current Density Magnitude using Neural Networkscited by 6
  4. 2022Reinforced Inverse Scatteringcited by 5
  5. 2023VI-DGP: A variational inference method with deep generative prior for solving high-dimensional inverse problemscited by 4
  6. 2023A Direct Sampling-Based Deep Learning Approach for Inverse Medium Scattering Problemscited by 4
  7. 2023Operator learning for hyperbolic partial differential equationscited by 4
  8. 2021Accurate and Robust Deep Learning Framework for Solving Wave-Based Inverse Problems in the Super-Resolution Regimecited by 3
  9. 2023Deep Injective Prior for Inverse Scatteringcited by 3
  10. 2024Back-Projection Diffusion: Solving the Wideband Inverse Scattering Problem with Diffusion Modelscited by 3
  11. 2025Self-composing neural operators for high-frequency and multiscale PDE surrogatescited by 3
  12. 2023Conductivity Imaging from Internal Measurements with Mixed Least-Squares Deep Neural Networkscited by 2
  13. 2022Solving the Wide-band Inverse Scattering Problem via Equivariant Neural Networkscited by 1
  14. 2024Physics-aware deep learning framework for the limited aperture inverse obstacle scattering problemcited by 1
  15. 2024Neumann Series-based Neural Operator for Solving Inverse Medium Problemcited by 1
  16. 2024Practical Aspects on Solving Differential Equations Using Deep Learning: A Primercited by 0
  17. 2025A physics informed neural network approach to simulating ice dynamics governed by the shallow ice approximationcited by 0
  18. 2025Deep Micro Solvers for Rough-Wall Stokes Flow in a Heterogeneous Multiscale Methodcited by 0
  19. 2025Efficient Tensor Completion Algorithms for Highly Oscillatory Operatorscited by 0
  20. 2025A Model-Guided Neural Network Method for the Inverse Scattering Problemcited by 0
  21. 2026Physics-Encoded Inverse Modeling for Arctic Snow Depth Estimationcited by 0
  22. 2026IV-Net: A neural network for elliptic PDEs with random and highly varying coefficientscited by 0
  23. 2026Cost-Accuracy Trade-offs: Neural Operator vs Classical Numerical Solvercited by 0