A stochastic machine-learned model for transition in high-speed boundary layers over a cone

Accurately predicting the laminar–turbulent transition in high-speed boundary layers is a longstanding challenge due to the nonlinear, chaotic dynamics and sensitivity to flow conditions. While high-fidelity simulations provide reliable data, their computational cost limits use in parametric studies or uncertainty quantification. Moreover, uncertainty in input parameters, such as environmental conditions or disturbance amplitude, can lead to predictions that differ qualitatively from the true transition scenarios in experiments and flight. We present a Bayesian machine learning framework that combines active learning with deep operator networks to predict transition onset while quantifying uncertainty. This approach enables targeted sampling of the most informative scenarios, optimizing training requirements and reducing predictive uncertainty. We demonstrate the method on high-speed boundary-layer flow over a 7-degree half-angle cone across varying flow conditions. The resulting model achieves orders-of-magnitude computational savings while maintaining predictive robustness.