Graph Feedforward Network (GFN) - a novel neural network layer for resolution-invariant machine learning

<p align="center"> <a href="https://doi.org/10.1016/j.cma.2024.117458"> <img src="https://badgen.net/badge/10.1016/j.cma.2024.117458/red?icon=github/" alt="doi"> </a> <!-- <a href="https://codecov.io/gh/Oisin-M/gfn"> <img src="https://codecov.io/gh/Oisin-M/gfn/branch/develop/graph/badge.svg" alt="Code Coverage"> </a> --> <a href="https://opensource.org/licenses/apache-2-0"> <img src="https://img.shields.io/badge/Licence-Apache 2.0-blue.svg" alt="Licence"> </a> <a href="https://github.com/Oisin-M/gfn/releases"> <img src="https://img.shields.io/github/v/release/Oisin-M/gfn?color=purple&label=Release" alt="Latest Release"> </a> </p> <p align="center"> <a href="#why-gfns">Why GFNs?</a> • <a href="https://gfn-layer.readthedocs.io">Documentation</a> • <a href="#installation">Installation</a> • <a href="#quickstart">Quickstart</a> • <a href="#citing">Citing</a> </p>

GFN is a generalisation of feedforward networks for graphical data.

[!IMPORTANT] The code reproducing the results in the GFN-ROM paper has now been moved to Oisin-M/GFN-ROM.

Why GFNs?

Many applications rely upon graphical data, which standard machine learning methods such as feedforward networks and convolutions cannot handle. GFNs present a novel approach of tackling this problem by extending existing machine learning approaches for use on graphical data. GFNs have very close links with neural operators and graph neural networks.

<p align="center"> <img src="https://github.com/Oisin-M/gfn/raw/refs/heads/main/docs/images/gfn.png"/> </p>

Key advantages of GFNs:

• Resolution invariance
• Equivalence to feedforward networks for single fidelity data (no deterioration in performance)
• Provable guarantees on performance for super- and sub-resolution
• Both fixed and adapative multifidelity training possible

Installation

gfn is readily available on PyPI.

pip install gfn-layer

Note: the package name on PyPI is gfn-layer, gfn refers to a different package.

Quickstart

See the user guide to get started!

Citing

If this work is useful to you, please cite

[1] Morrison, O. M., Pichi, F. and Hesthaven, J. S. (2024) ‘GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications’. Available at: arXiv and Computer Methods in Applied Mechanics and Engineering

@article{Morrison2024,
  title = {{GFN}: {A} graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications},
  author = {Morrison, Oisín M. and Pichi, Federico and Hesthaven, Jan S.},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {432},
  pages = {117458},
  year = {2024},
  doi = {10.1016/j.cma.2024.117458},
}