Bayesian Inversion and Uncertainty Quantification for Hypersonic Flows

Hypersonic flow fields exhibit significant parametric and model-form uncertainties, while the high computational cost of resolving the associated multi-physics limits the feasibility of brute-force uncertainty quantification. At the same time, experimental data in these regimes tend to be sparse and frequently provide only indirect observations of the quantities of interest. This work presents a computational framework for Bayesian inference in hypersonic flow simulations that enables efficient estimation of the probability distributions of uncertain parameters using a limited number of noisy measurements. The prior distribution of the unknown parameters is modeled using a finite mixture of Gaussian densities, providing a flexible and expressive parametric representation capable of capturing nonlinear and multimodal parameter dependencies. Assuming additive Gaussian measurement noise, we formulate a likelihood based on the discrepancy between the observed data and CFD-predicted quantities of interest, and perform posterior inference to obtain statistically consistent parameter estimates along with quantified uncertainty bounds. The framework integrates efficiently with existing CFD solvers, requiring only modest modifications to the forward-model infrastructure while enabling exploration of complex posterior densities. The method is verified on canonical inverse problems demonstrating accurate recovery of multimodal posteriors, and then applied to infer free-stream conditions from sparse surface measurements on a cone geometry tested in a hypersonic wind tunnel. The inferred parameters yield improved agreement with experimental heat flux data in both turbulent and laminar regions of the flow.