mlsanityData to 7 Oct 2026

Meta-learning Pseudo-differential Operators with Deep Neural Networks

arXiv 1906.06782 ↗First posted 16 Jun 2019math.NA cs.LG cs.NAcited by 17

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Abstract (arXiv)

This paper introduces a meta-learning approach for parameterized pseudo-differential operators with deep neural networks. With the help of the nonstandard wavelet form, the pseudo-differential operators can be approximated in a compressed form with a collection of vectors. The nonlinear map from the parameter to this collection of vectors and the wavelet transform are learned together from a small number of matrix-vector multiplications of the pseudo-differential operator. Numerical results for Green's functions of elliptic partial differential equations and the radiative transfer equations demonstrate the efficiency and accuracy of the proposed approach.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 16 Jun 2019.

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Citing papers per year: 2021: 6; 2022: 4; 2023: 3; 2024: 2; 2025: 1; 2026: 1.

17 papers.

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  1. 2021Multiwavelet-based Operator Learning for Differential Equationscited by 229
  2. 2023A Mathematical Guide to Operator Learningcited by 74
  3. 2021Data-driven discovery of Green's functions with human-understandable deep learningcited by 43
  4. 2021Learning elliptic partial differential equations with randomized linear algebracited by 29
  5. 2022Learning Green's functions associated with time-dependent partial differential equationscited by 25
  6. 2022Guiding continuous operator learning through Physics-based boundary constraintscited by 21
  7. 2024Operator Learning Using Random Features: A Tool for Scientific Computingcited by 21
  8. 2022Minimax Optimal Kernel Operator Learning via Multilevel Trainingcited by 13
  9. 2024Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learningcited by 10
  10. 2022Principled Acceleration of Iterative Numerical Methods Using Machine Learningcited by 6
  11. 2021Deep Microlocal Reconstruction for Limited-Angle Tomographycited by 4
  12. 2023Inverse Problems with Learned Forward Operatorscited by 4
5 more
  1. 2023Operator learning for hyperbolic partial differential equationscited by 4
  2. 2025Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approachcited by 1
  3. 2021How many moments does MMD compare?cited by 0
  4. 2021Learning the structure of wind: A data-driven nonlocal turbulence model for the atmospheric boundary layercited by 0
  5. 2026Windowed Fourier Propagator: A Frequency-Local Neural Operator for Wave Equations in Inhomogeneous Mediacited by 0