A resolution-invariant generalisation of feedforward networks for graphical data, applied to model order reduction (MOR).

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.

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

We show the capability of GFNs for MOR by developing the graph feedforward network reduced order model (GFN-ROM).

Key advantages of GFN-ROM:

• First graph-based resolution-invariant ROM
• Lightweight and flexible architecture
• Computational efficiency
• Excellent generalisation performance
• Adaptive multifidelity training

The code implementing the GFN-ROM model is given in

• gfn_rom/

All results presented in the paper are fully reproducible and we provide pre-run jupyter notebooks containing all the necessary code in

• graetz/
• advection/
• stokes/

Requirements: Running GFN-ROM requires

• torch, numpy, sklearn, matplotlib, tqdm, pykdtree

Additional modules are required if one wishes to rerun the data generation or GCA-ROM experiments.

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

@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={arXiv preprint arXiv:2406.03569},
  year={2024}
}