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We contribute to the vastly growing field of machine learning for engineeringsystems by demonstrating that equivariant graph neural networks have thepotential to learn more accurate dynamic-interaction models than theirnon-equivariant counterparts. We benchmark two well-studied fluid flow systems,namely the 3D decaying Taylor-Green vortex and the 3D reverse Poiseuille flow,and compare equivariant graph neural networks to their non-equivariantcounterparts on different performance measures, such as kinetic energy orSinkhorn distance. Such measures are typically used in engineering to validatenumerical solvers. Our main findings are that while being rather slow to trainand evaluate, equivariant models learn more physically accurate interactions.This indicates opportunities for future work towards coarse-grained models forturbulent flows, and generalization across system dynamics and parameters.

E($3$) Equivariant Graph Neural Networks for Particle-Based Fluid Mechanics