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A learned Born series for highly-scattering media.

Antonio Stanziola1, Simon Arridge1, Ben T Cox1

  • 1University College London, Gower Street, London, WC1E 6BT, United Kingdoma.stanziola@ucl.ac.uk, s.arridge@ucl.ac.uk, b.cox@ucl.ac.uk, b.treeby@ucl.ac.uk.

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A novel learned Born series (LBS) method improves wave equation solutions. This AI-driven approach offers superior accuracy for high-contrast problems with fewer iterations compared to traditional methods.

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Area of Science:

  • Computational physics
  • Numerical analysis
  • Wave phenomena

Background:

  • Solving the wave equation is crucial in many scientific fields.
  • Traditional methods like the convergent Born series can be computationally intensive and less accurate for complex scenarios.
  • High contrast scatterers pose a significant challenge for existing numerical techniques.

Purpose of the Study:

  • To introduce a new, data-driven method for solving the wave equation.
  • To enhance accuracy and efficiency in wave field prediction, particularly for challenging media.
  • To leverage machine learning to improve upon established numerical series expansions.

Main Methods:

  • Development of the learned Born series (LBS) by training components of a convergent Born series.
  • Iterative application of the LBS to solve the wave equation.
  • Comparative analysis against the standard convergent Born series.

Main Results:

  • The LBS demonstrates significantly higher accuracy than the convergent Born series for the same number of iterations.
  • This improved performance is particularly evident when dealing with high contrast scatterers.
  • The LBS achieves a reasonable prediction of the global pressure field with few iterations, with errors diminishing as iterations increase.
  • Computational complexity remains comparable to the traditional method.

Conclusions:

  • The learned Born series (LBS) offers a more accurate and efficient approach to solving the wave equation.
  • LBS shows particular promise for inverse scattering problems and wave field simulations in complex media.
  • This data-driven method represents a significant advancement in computational wave physics.