Generative Deep Learning Models for Supersonic and Hypersonic Flow Fields

The numerical solution of partial differential equations is fundamental to a wide range of engineering applications. Many numerical schemes struggle to accurately capture discontinuities in the solution and either require very high spatial and temporal resolution, or the introduction of stabilization techniques which can severely compromise accuracy. In particular, for supersonic and hypersonic flows, this makes them computationally expensive to run. In recent years, the use of machine learning in fluid dynamics has sparked considerable interest. However, investigations into the application of neural networks to supersonic and hypersonic regimes remain extremely limited. This paper compares the performance of Convolutional Neural Networks (CNNs) and Graph Neural Networks (GNNs) for performing inference in such flows. The study considers a wide range of Mach numbers, angles of attack, and object geometries to capture key phenomena such as bow shocks, expansion waves, and oblique shocks. Several neural network configurations and anti-over-smoothing strategies are evaluated and compared. Results have shown that the proposed networks are able to reduce computational time by three to five orders of magnitude while maintaining an R^2 consistently above 0.99 for unseen datasets within the training ranges and above 0.9 for unseen datasets beyond the training ranges.