# Meta-learning Pseudo-differential Operators with Deep Neural Networks

arXiv: https://arxiv.org/abs/1906.06782 · HTML: https://mlsanity.com/paper/1906.06782/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2019.

## Built on by (most cited first, 17 of 17)

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- [Inverse Problems with Learned Forward Operators](https://mlsanity.com/paper/2311.12528/) (2023)
- [Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approach](https://mlsanity.com/paper/2506.05245/) (2025)
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- [Learning the structure of wind: A data-driven nonlocal turbulence model for the atmospheric boundary layer](https://mlsanity.com/paper/2107.11046/) (2021)
- [Windowed Fourier Propagator: A Frequency-Local Neural Operator for Wave Equations in Inhomogeneous Media](https://mlsanity.com/paper/2603.14289/) (2026)

## 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.