# Neural Born Iteration Method For Solving Inverse Scattering Problems: 2D Cases

arXiv: https://arxiv.org/abs/2112.09831 · HTML: https://mlsanity.com/paper/2112.09831/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 51 references that are in the map.
- First posted on arXiv 18 Dec 2021.

## Builds on (most cited first, 9 of 9)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Deep Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/1804.04272/) (2018)
- [Dynamical Isometry and a Mean Field Theory of CNNs: How to Train 10,000-Layer Vanilla Convolutional Neural Networks](https://mlsanity.com/paper/1806.05393/) (2018)
- [DeepNIS: Deep Neural Network for Nonlinear Electromagnetic Inverse Scattering](https://mlsanity.com/paper/1810.03990/) (2018)
- [Dynamical Isometry is Achieved in Residual Networks in a Universal Way for any Activation Function](https://mlsanity.com/paper/1809.08848/) (2018)

## Built on by (most cited first, 9 of 9)

- [Physics Embedded Machine Learning for Electromagnetic Data Imaging](https://mlsanity.com/paper/2207.12607/) (2022)
- [Physics-Driven Neural Network for Solving Electromagnetic Inverse Scattering Problems](https://mlsanity.com/paper/2507.16321/) (2025)
- [Deep Injective Prior for Inverse Scattering](https://mlsanity.com/paper/2301.03092/) (2023)
- [Multi-frequency Neural Born Iterative Method for Solving 2-D Inverse Scattering Problems](https://mlsanity.com/paper/2409.01315/) (2024)
- [Improved Physics-Driven Neural Network to Solve Inverse Scattering Problems](https://mlsanity.com/paper/2512.09333/) (2025)
- [VBIM-Net: Variational Born Iterative Network for Inverse Scattering Problems](https://mlsanity.com/paper/2405.18731/) (2024)
- [A Differentiable Framework for Full and Phaseless Data Inversion Using Neural Implicit Contrast-Source Representation](https://mlsanity.com/paper/2508.10555/) (2025)
- [Coordinate-Residual Physics-Driven Neural Network for Inverse Scattering Imaging](https://mlsanity.com/paper/2608.09382/) (2026)
- [Structured Multi-Level-Set Inversion for 3-D Electromagnetic Inverse Scattering](https://mlsanity.com/paper/2609.08594/) (2026)

## Abstract (arXiv)

In this paper, we propose the neural Born iterative method (NeuralBIM) for solving 2D inverse scattering problems (ISPs) by drawing on the scheme of physics-informed supervised residual learning (PhiSRL) to emulate the computing process of the traditional Born iterative method (TBIM). NeuralBIM employs independent convolutional neural networks (CNNs) to learn the alternate update rules of two different candidate solutions regarding the residuals. Two different schemes are presented in this paper, including the supervised and unsupervised learning schemes. With the data set generated by the method of moments (MoM), supervised NeuralBIM are trained with the knowledge of total fields and contrasts. Unsupervised NeuralBIM is guided by the physics-embedded objective function founding on the governing equations of ISPs, which results in no requirement of total fields and contrasts for training. Numerical and experimental results further validate the efficacy of NeuralBIM.