Computationally effective estimation of supersonic flow field around airfoils using sparse convolutional neural network

This work proposes an innovative approach for supersonic flow field modeling around airfoils based on sparse convolutional neural networks (SCNNs) and Bézier generative adversarial network (GAN), where (1) the SCNN model is built to end-to-end predict supersonic compressible physical flow fields around airfoils from spatially-sparse geometries and (2) the trained Bézier-GAN is utilized to generate plenty of smooth airfoils as well as the latent codes representing airfoils. The spatially-sparse positions of airfoil geometry are represented using signed distance function (SDF). Particularly, the latent codes are merged with the SDF matrix and the Mach number to form the input of the SCNN model, effectively making the SCNN model possess more robust geometric adaptability to different flow conditions. The most significant contribution compared to the regular convolutional neural network is that SCNN introduces sparse convolutional operations to process spatially-sparse input matrix, specifically, which only focuses on the local area with flow information when performing convolution, eventually saving memory usage and improving the network’s attention on the flow area. Further, the testing results show that the SCNN model can more accurately predict supersonic flow fields with a mean absolute error lower than 5% and save 40% of graphics processing unit memory. These results indicate that the proposed SCNN model can capture the shock wave features of supersonic flow fields and improve learning efficiency and computing efficiency.