# A Learned Born Series for Highly-Scattering Media

arXiv: https://arxiv.org/abs/2212.04948 · HTML: https://mlsanity.com/paper/2212.04948/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 17 references that are in the map.
- First posted on arXiv 9 Dec 2022.

## Builds on (most cited first, 6 of 6)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [A Helmholtz equation solver using unsupervised learning: Application to transcranial ultrasound](https://mlsanity.com/paper/2010.15761/) (2020)
- [j-Wave: An open-source differentiable wave simulator](https://mlsanity.com/paper/2207.01499/) (2022)

## Built on by (most cited first, 3 of 3)

- [Neural Born Series Operator for Biomedical Ultrasound Computed Tomography](https://mlsanity.com/paper/2312.15575/) (2023)
- [Learning Greens Operators through Hierarchical Neural Networks Inspired by the Fast Multipole Method](https://mlsanity.com/paper/2509.20591/) (2025)
- [Survey of Deep Learning and Physics-Based Approaches in Computational Wave Imaging](https://mlsanity.com/paper/2410.08329/) (2024)

## Abstract (arXiv)

A new method for solving the wave equation is presented, called the learned Born series (LBS), which is derived from a convergent Born Series but its components are found through training. The LBS is shown to be significantly more accurate than the convergent Born series for the same number of iterations, in the presence of high contrast scatterers, while maintaining a comparable computational complexity. The LBS is able to generate a reasonable prediction of the global pressure field with a small number of iterations, and the errors decrease with the number of learned iterations.