Keywords: Graph neural networks, Equivariance, Invariance, Fluid dynamics
TL;DR: We explore equivariant graph neural network architectures in the context of fluid flow forecasting and find that invariant representations are key to effective modeling.
Abstract: Graph neural networks (GNNs) have shown promise in learning unstructured mesh-based simulations of physical systems, including fluid dynamics. In tandem, geometric deep learning principles have informed the development of equivariant architectures. However, the practical implications of rotational equivariance in modeling fluids remains under-explored. We build a multi-scale equivariant GNN to forecast buoyancy-driven shear fluid flow and study the effect of modeling invariant and non-invariant representations of the flow state. Our results show that modeling invariant quantities produces more accurate long-term predictions and that these invariant quantities may be learned from the velocity field using a data-driven encoder.