ML for fast assimilation of wall-pressure measurements from hypersonic flow over a cone*

The performance of hypersonic vehicles is sensitive to environmental disturbances, especially in the transitional flow regime. Accurate and efficient prediction of the flow state from limited sensor data is a pacing item in both fundamental studies and practical applications. Recent data assimilation demonstrated the integration of scarce measurements into direct numerical simulations (Buchta et al, J. Fluid Mech., 947, R2, 2022). Solving the inverse problem unveiled the realistic flow hidden within limited measurements, granting access to every flow quantity. However, the computational cost associated with direct simulations hinders wide adoption, for example for a large number of experiments or in practical applications. Here, we introduce a deep-learning approach that can accelerate assimilation by two orders of magnitude in terms of the number of experiments assimilated using the same wall-clock time.  We minimize the number of required numerical simulations by optimally sampling the space of possible solutions, deploy a deep operator network (DeepONet) as proxy of the compressible Navier-Stokes equations to continuously span and search high-dimensional noisy spaces of solutions, and efficiently reach an optimal result with a gradient-free technique. The successful application of this method is demonstrated for data assimilation of wind-tunnel measurements in boundary-layer flow over a 7-degree half-angle cone, at Mach 6.