A novel graph modeling method for GNN-based hypersonic aircraft flow field reconstruction

Detection of flow fields constitutes a critical role in the advancement and innovation of hypersonic aircraft. Under hypersonic conditions, aircraft aerodynamics manifest a multitude of complex phenomena, including intense turbulence and fluctuations, transitions within the boundary layer, interactions between shock waves and boundary layers, as well as the effects of high-temperature gas. Thus, the surveillance of hypersonic aircraft flow fields is imperative not only for flight safety but also for the progression of hypersonic technologies. Given the practical limitations that restrict sensors installed to only key areas for detection, we propose a GNN-based method for hypersonic aircraft flow field reconstruction from limited sensors. Moreover, we have introduced a novel graph modeling technique for enhancing the reconstruction motivated by that solely the most significant edges within the graph are efficacious for field reconstruction. The methodology encompasses the following steps, modeling graphs from diverse perspectives, and transforming them into minimum spanning trees. These sparse graphs are then integrated with learnable weights optimized by automatic differentiation. Our method has been tested on an open-source turbulence dataset, the two components of graph pruning and weight optimization bring about 34% and 10% improvements on average. Furthermore, our approach has been validated in the reconstruction of hypersonic aircraft flow fields for at least 10% error reduction among all the situations.