Flexible SE(2) graph neural networks with applications to PDE surrogates
<|reference_start|>Flexible SE(2) graph neural networks with applications to PDE surrogates: 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.<|reference_end|>
@article{bånkestad2024flexible,
    title={Flexible SE(2) graph neural networks with applications to PDE surrogates},
    author={Maria B{aa}nkestad, Olof Mogren, Aleksis Pirinen},
    journal={arXiv preprint arXiv:2405.20287},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.20287},
    primaryClass={cs.LG cs.AI cs.NA math.NA physics.flu-dyn}
}