Graph Rewiring based on Flow Alignment for Improving Fluid Simulation

To overcome the computational burden of traditional computational fluid dynamics (CFD), graph neural network-based (GNN) learned simulators have attracted growing interest because they naturally operate on CFD meshes. However, classical GNNs only exchange information between neighbouring nodes, limiting flow prediction accuracy. While graph rewiring can improve information propagation, existing methods are mostly designed for generic graphs, and PIORF relies on long-range connections for fluid simulation. In this work, we show that simply connecting all 2-hop nodes can already achieve competitive performance with PIORF, raising questions about the necessity of distant rewiring. Motivated by fluid transport principles, we propose Flow Alignment Rewiring (FLARE), a simple and efficient local rewiring method that connects 2-hop nodes only when their relative direction aligns with the input flow direction. Hence, FLARE is a physics-informed local rewiring method, different from PIORF and well-aligned with fluid physics. Extensive numerical experiments on flows over a cylinder, single-, and tandem-airfoil under different flow conditions and deep network architectures demonstrate that FLARE outperforms PIORF and various 2-hop rewiring approaches by a significant margin.