Forward and inverse problems in high-speed boundary layers using DeepONets

Fast prediction of instability waves in high-speed boundary layers is numerically challenging. We show how DeepONets, deep neural network architectures designed to approximate operators, can be used to (1) map an incoming perturbation to its corresponding downstream field accurately and (2) determine the original perturbation out of downstream measurements. Moreover, we show that informing the training of the DeepONet with the continuity equation improves the accuracy of the results. We trained the DeepONets using data generated from solutions of the linear parabolized stability equations and from direct numerical simulations of the compressible Navier-Stokes equations. These results are a necessary step towards to application of neural-network technology to more complex high-speed flow configurations and to data assimilation problems.