Transition prediction in high-speed boundary layers using Bayesian neural operators

Accurate prediction of laminar-to-turbulent transition in high-speed boundary layers is essential for the design and performance assessment of supersonic vehicles. This study presents a novel approach that integrates Bayesian deep operator neural networks (Bayesian DeepONet) with an active learning framework to predict transition Reynolds numbers and quantify associated uncertainties. While deterministic DeepONet models require extensive datasets from direct numerical simulations (DNS) and lack inherent uncertainty quantification, the Bayesian formulation enables probabilistic predictions through Bayesian inference. To reduce the computational cost of training-data generation, an active learning strategy based on uncertainty sampling is employed and enhanced with a local exclusion criterion. The proposed methodology is applied to a high-speed flat plate boundary layer, where transition Reynolds numbers are inferred from free-stream Mach numbers and upstream spectral information.