Flexible SE(2) graph neural networks with applications to PDE surrogates

Maria Bånkestad, Olof Mogren, Aleksis Pirinen
5/30/2024
cs.LGcs.AImath.NA

No official code found. Best implementation: mariabankestad/SE2-GNN (4 stars, last commit 2024-06-03).

Abstract

This paper presents a novel approach for constructing graph neural networks equivariant to 2D rotations and translations and leveraging them as PDE surrogates on non-gridded domains. We show that aligning the representations with the principal axis allows us to sidestep many constraints while preserving SE(2) equivariance. By applying our model as a surrogate for fluid flow simulations and conducting thorough benchmarks against non-equivariant models, we demonstrate significant gains in terms of both data efficiency and accuracy.

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Code Implementations(1)

mariabankestad/SE2-GNNCommunity100%

An SE(2) equivariant graph neural network.

40Python, Jupyter NotebookMay 29, 20242 years ago

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Cite this paper

@article{bnkestad2024flexible,
  title  = {Flexible SE(2) graph neural networks with applications to PDE surrogates},
  author = {Maria Bånkestad and Olof Mogren and Aleksis Pirinen},
  year   = {2024},
  eprint = {2405.20287},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2405.20287v1}
}

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