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 preser...

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Bibliographic Details
Main Authors:	Bånkestad, Maria, Mogren, Olof, Pirinen, Aleksis
Format:	Journal Article
Language:	English
Published:	30-05-2024
Subjects:	Computer Science - Artificial Intelligence Computer Science - Learning Computer Science - Numerical Analysis Mathematics - Numerical Analysis Physics - Fluid Dynamics
Online Access:	Get full text
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Summary:	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.
DOI:	10.48550/arxiv.2405.20287