Neural incomplete factorization

This repository contains the code for learning incomplete factorization preconditioners directly from data by Paul Häusner, Aleix Nieto Juscafresa, Ozan Öktem, and Jens Sjölund.

Installation

In order to run the training and testing, you need to install the following python dependencies:

• pytorch
• pytorch-geometric
• scipy
• networkx

For validation and testing the following packages are required:

• matplotlib
• numml (for efficient forward-backward substitution)
• ilupp (for baseline incomplete factorization preconditioners)

Implementation

The repository consists of several parts. In the krylov folder implementations for the conjugate gradient method and GRMES method are provided. Further, several preconditioner (Jacobi, ILU, IC) are implemented.

The neuralif module contains the code for the learned preconditioner. The model.py file contains the different models that can be utilizes, loss.py implements several different loss functions.

A synthetic dataset is provided in the folder apps.

References

If our code helps your research or work, please consider citing our paper. The following are BibTeX references:

@article{hausner2024neural,
  title={Neural incomplete factorization: learning preconditioners for the conjugate gradient method},
  author={Paul H{\"a}usner and Ozan {\"O}ktem and Jens Sj{\"o}lund},
  journal={Transactions on Machine Learning Research},
  issn={2835-8856},
  year={2024},
  url={https://openreview.net/forum?id=FozLrZ3CI5}
}

@InProceedings{hausner2025learning,
  title={Learning incomplete factorization preconditioners for {GMRES}},
  author={H{\"a}usner, Paul and Nieto Juscafresa, Aleix and Sj{\"o}lund, Jens},
  booktitle={Proceedings of the 6th Northern Lights Deep Learning Conference (NLDL)},
  pages={85--99},
  year={2025},
  volume={265},
  series={Proceedings of Machine Learning Research},
  publisher={PMLR},
}

Please feel free to reach out if you have any questions or comments.

Contact: Paul Häusner, [email protected]