mlsanityData to 14 Oct 2026

A Learned Born Series for Highly-Scattering Media

arXiv 2212.04948 ↗First posted 9 Dec 2022physics.comp-ph cs.LG physics.med-phcited by 3

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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.

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

6 of 17 references.

References · 6

  1. 2016Gaussian Error Linear Units (GELUs)cited by 3,502
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2019Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processingcited by 421
  4. 2021Neural Operator: Learning Maps Between Function Spacescited by 414
  5. 2020A Helmholtz equation solver using unsupervised learning: Application to transcranial ultrasoundcited by 12
  6. 2022j-Wave: An open-source differentiable wave simulatorcited by 9

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Cited by year

Citing papers per year: 2023: 1; 2024: 1; 2025: 1.

3 papers.

  1. 2023Neural Born Series Operator for Biomedical Ultrasound Computed Tomographycited by 3
  2. 2025Learning Greens Operators through Hierarchical Neural Networks Inspired by the Fast Multipole Methodcited by 2
  3. 2024Survey of Deep Learning and Physics-Based Approaches in Computational Wave Imagingcited by 0