Multi-scale rotation-equivariant graph neural networks for unsteady Eulerian fluid dynamics

The simulation of fluid dynamics, typically by numerically solving partial differential equations, is an essential tool in many areas science and engineering. However, the high computational cost can limit application practice may prohibit exploring large parameter spaces. Recent deep-learning approaches have demonstrated potential to yield surrogate models for dynamics. While such exhibit lower accuracy comparison, their low runtime makes them appealing design-space exploration. We introduce two novel graph neural network (GNN) models, multi-scale (MuS)-GNN rotation-equivariant (RE) MuS-GNN, extrapolating time evolution flow. In both previous states are processed through multiple coarsening graph, which enables faster information propagation improves capture forecast system state, particularly problems encompassing phenomena spanning a range length scales. Additionally, REMuS-GNN architecturally equivariant rotations, allows learn underlying physics more efficiently, leading improved generalization. analyze these using canonical models: advection incompressible Our results show that proposed GNN generalize from uniform fields high-gradient on complex domains. architecture inference Navier–Stokes solutions, within Reynolds numbers design parameters, effectively than baseline single-scale GNN. Simulations obtained with MuS-GNN between four orders magnitude numerical solutions they were trained.