Neural Operators & PDE Solvers Reading List

Curated by Mouhssine Rifaki | Stanford Electrical Engineering | Last updated August 2026

Neural operators learn mappings between function spaces, making them natural solvers for parametric PDEs. This list moves from universal approximation and PINNs to Fourier and DeepONet operators.

Neural Operators & PDE Solvers: 10 key papers

1. Fourier Neural Operator for Parametric Partial Differential Equations
   Li et al. arXiv 2020.
2. Neural Operator: Learning Maps Between Function Spaces
   Kovachki et al. arXiv 2021.
3. DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
   Lu et al. arXiv 2019.
4. Physics-Informed Neural Operator for Learning Partial Differential Equations
   Li et al. arXiv 2021.
5. Factorized Fourier Neural Operators
   Tran et al. arXiv 2021.
6. Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers
   Guibas et al. arXiv 2021.
7. U-NO: U-shaped Neural Operators
   Rahman et al. arXiv 2022.
8. Convolutional Neural Operators for robust and accurate learning of PDEs
   Raonić et al. arXiv 2023.
9. Transformer for Partial Differential Equations' Operator Learning
   Li et al. arXiv 2022.
10. Message Passing Neural PDE Solvers
    Brandstetter et al. arXiv 2022.

Related reading lists

• Physics-Informed Machine Learning & Scientific ML
• Linear MDPs & Linear Function Approximation
• Graph Neural Networks & Message Passing
• Neural ODEs & Continuous-Time Models
• Kernel Methods & RKHS
• Privacy & Differential Privacy in Machine Learning
• Score-Based Generative Modeling
• Transformers for Sequential Decision Making