  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 respecting underlying physical symmetries. However,
the effect of rotational equivariance in modeling fluids remains unclear. We
build a multi-scale equivariant GNN to forecast fluid flow and study the effect
of modeling invariant and non-invariant representations of the flow state. We
evaluate the model performance of several equivariant and non-equivariant
architectures on predicting the evolution of two fluid flows, flow around a
cylinder and buoyancy-driven shear flow, to understand the effect of
equivariance and invariance on data-driven modeling approaches. 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.
