mlsanityData to 14 Oct 2026

Scattering with Neural Operators

arXiv 2308.14789 ↗First posted 28 Aug 2023hep-th cs.LG physics.comp-phcited by 7

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Abstract (arXiv)

Recent advances in machine learning establish the ability of certain neural-network architectures called neural operators to approximate maps between function spaces. Motivated by a prospect of employing them in fundamental physics, we examine applications to scattering processes in quantum mechanics. We use an iterated variant of Fourier neural operators to learn the physics of Schr"odinger operators, which map from the space of initial wave functions and potentials to the final wave functions. These deep operator learning ideas are put to test in two concrete problems: a neural operator predicting the time evolution of a wave packet scattering off a central potential in 1+1 dimensions, and the double-slit experiment in 2+1 dimensions. At inference, neural operators can become orders of magnitude more efficient compared to traditional finite-difference solvers.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 24 of its 45 references that are in the map. First posted on arXiv 28 Aug 2023.

Builds on

24 of 45 references.

References · 24

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  3. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  4. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
  5. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 427
  6. 2021Neural Operator: Learning Maps Between Function Spacescited by 414
  7. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 349
  8. 2021Choose a Transformer: Fourier or Galerkincited by 343
  9. 2020Model Reduction and Neural Networks for Parametric PDEscited by 258
  10. 2021Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformerscited by 248
  11. 2021Multiwavelet-based Operator Learning for Differential Equationscited by 234
  12. 2022U-NO: U-shaped Neural Operatorscited by 230
12 more
  1. 2022MIONet: Learning multiple-input operators via tensor productcited by 181
  2. 2017Sobolev Training for Neural Networkscited by 143
  3. 2022Physics-Informed Deep Neural Operator Networkscited by 113
  4. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  5. 2022Generic bounds on the approximation error for physics-informed (and) operator learningcited by 65
  6. 2022Reliable extrapolation of deep neural operators informed by physics or sparse observationscited by 62
  7. 2023Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustnesscited by 60
  8. 2022Generative Adversarial Neural Operatorscited by 52
  9. 2021Machine Learning in the Search for New Fundamental Physicscited by 50
  10. 2023Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestrationcited by 46
  11. 2023Real-time Inference and Extrapolation via a Diffusion-inspired Temporal Transformer Operator (DiTTO)cited by 16
  12. 2022Semi-supervised Learning of Partial Differential Operators and Dynamical Flowscited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 4; 2025: 2; 2026: 1.

7 papers.

  1. 2024Learning S-Matrix Phases with Neural Operatorscited by 3
  2. 2024Neural Quantum Propagators for Driven-Dissipative Quantum Dynamicscited by 3
  3. 2024Fourier Neural Operators for Learning Dynamics in Quantum Spin Systemscited by 2
  4. 2026Is Zero-Shot Super-Resolution Possible in Operator Learning?cited by 1
  5. 2024Neural Hamilton: Can A.I. Understand Hamiltonian Mechanics?cited by 0
  6. 2025Operator Learning for Schr"odinger Equation: Unitarity, Error Bounds, and Time Generalizationcited by 0
  7. 2025Symmetry and Generalisation in Neural Approximations of Renormalisation Transformationscited by 0