This repository contains the main algorithm of the paper "Linearization Turns Neural Operators into Function-Valued Gaussian Processes" by Magnani et al. (2025).

luno is a Python package that implements linearized uncertainty quantification for neural operators. It provides tools for:

• Fourier Neural Operators with uncertainty quantification
• Jacobian computations for Fourier Neural Operators
• Covariance structures for function-valued Gaussian processes

The package can be installed via pip:

pip install git+https://github.com/MethodsOfMachineLearning/luno.git

For development installation with all dependencies:

pip install -e ".[dev]"

If you use this code in your research, please cite:

@misc{magnani2025linearizationturnsneuraloperators,
      title={Linearization Turns Neural Operators into Function-Valued Gaussian Processes}, 
      author={Emilia Magnani and Marvin Pförtner and Tobias Weber and Philipp Hennig},
      year={2025},
      eprint={2406.05072},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2406.05072}
}

• Python >= 3.10
• NumPy >= 1.21.2
• JAX <= 0.4.48
• linox (from GitHub)

Optional dependencies for development and testing are available in the dev extra.