Assimilation of wall-pressure measurements in high-speed boundary layers using a Bayesian-ML approach

Assimilation of wall-pressure measurements in high-speed flows was previously successfully demonstrated using ensemble variational (EnVar) techniques, for flat plate boundary layers (Buchta & Zaki, J. Fluid Mech., 916, A44, 2021) and flow over a slender cone (Buchta et al. J. Fluid Mech., 947, R2, 2022). The EnVar technique is accurate, does not require an adjoint algorithm, and can be adopted with any forward model. However, success is highly dependent on the choice of the initial estimate of the unknown control vector. In this study, we develop a global optimizer for data assimilation using a Bayesian approach coupled with deep operator networks (DeepONets). Bayesian optimization minimizes the loss function by progressively incorporating measurements obtained from new estimates. A Gaussian process regression (GPR) is adopted as an estimator of the loss function, for which we adopt an ensemble of DeepONets. Performance is assessed in the context of high-speed boundary layer undergoing transition due to subharmonic resonance of planar and oblique instability waves. Using our combined Bayesian-DeepONet algorithm, the dominant frequency and phase difference between the 2D and 3D waves are estimated with satisfactory accuracy and efficiency.