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

2024/05/30 by Bånkestad, Maria, Mogren, Olof, Pirinen, Aleksis
#Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Machine Learning (cs.LG) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2405.20287

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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