mlsanityData to 7 Oct 2026

Hybrid operator learning of wave scattering maps in high-contrast media

arXiv 2602.11197 ↗First posted 30 Jan 2026eess.SP cs.AI cs.CVcited by 1

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Abstract (arXiv)

Surrogate modeling of wave propagation and scattering (i.e. the wave speed and source to wave field map) in heterogeneous media has significant potential in applications such as seismic imaging and inversion. High-contrast settings, such as subsurface models with salt bodies, exhibit strong scattering and phase sensitivity that challenge existing neural operators. We propose a hybrid architecture that decomposes the scattering operator into two separate contributions: a smooth background propagation and a high-contrast scattering correction. The smooth component is learned with a Fourier Neural Operator (FNO), which produces globally coupled feature tokens encoding background wave propagation; these tokens are then passed to a vision transformer, where attention is used to model the high-contrast scattering correction dominated by strong, spatial interactions. Evaluated on high-frequency Helmholtz problems with strong contrasts, the hybrid model achieves substantially improved phase and amplitude accuracy compared to standalone FNOs or transformers, with favorable accuracy-parameter scaling.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 19 of its 62 references that are in the map. First posted on arXiv 30 Jan 2026.

Builds on

19 of 62 references.

References · 19

  1. 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 4,993
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  3. 2021Swin Transformer V2: Scaling Up Capacity and Resolutioncited by 1,215
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  7. 2022Transformer for Partial Differential Equations' Operator Learningcited by 270
  8. 2021Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformerscited by 237
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  12. 2022Continuous PDE Dynamics Forecasting with Implicit Neural Representationscited by 71
7 more
  1. 2023PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networkscited by 62
  2. 2023Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustnesscited by 60
  3. 2025Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domainscited by 56
  4. 2023Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equationcited by 32
  5. 2024A Library for Learning Neural Operatorscited by 31
  6. 2024Mixtures of Neural Operators Reduce Active Complexity in Operator Learningcited by 16
  7. 2022LordNet: An Efficient Neural Network for Learning to Solve Parametric Partial Differential Equations without Simulated Datacited by 10

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Optimal Multiscale Learning of Linear Operatorscited by 0