Title: Graph Rewiring based on Flow Alignment for Improving Fluid Simulation
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Physics-informed Graph Neural Networks; CFD; mesh; rewiring; unsteady flow

Abstract: To overcome computation burden of traditional computational fluid dynamics (CFD) simulations, researchers have explored different architectures to develop physics-informed simulation methods. Among them, graph neural networks (GNN) are most suitable for adopting CFD meshes, which are extensively used in engineering and industrial applications. However, classical GNNs propagate information among neighbour nodes, which highly restrict information exchange within the network. To address this issue, graph rewiring methods have been developed for generic graph problems, but not particular for fluid simulation. PIORF, introducing edges connecting distant nodes, is the first graph rewiring method to do so, and previous experiments have demonstrated its effectiveness against state-of-the-art generic rewiring methods. Nevertheless, in this work, we found that simply connecting all 2-hop nodes can provide competitive performance with PIORF. This result raises three questions: 1) Is physics-informed rewiring really useful for improving flow predictions? 2) Should we consider just local connection, instead of connecting distant nodes? 3) Do we need to change the connections based on input flow for rollout simulations? By thoroughly adopting physical fluid principles, we propose a simple yet very efficient method, Flow Alignment Rewiring (FLARE) technique, which connects 2-hop nodes only when the node direction aligns with 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 and 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.