Machine-learning-enhanced structural-ensemble-dynamics-based stress-length model for transition prediction in hypersonic cone boundary layers

Accurate prediction of hypersonic transitional boundary layer (HTrBL) transition is critical for high-speed vehicle design but remains challenging due to complex, multi-factor characteristics of the flow. This study develops a data-driven framework integrating machine learning (ML) with Structural Ensemble Dynamics (SED) theory to enhance the SED-based stress-length transition model for sharp cones, addressing the key challenge of accurately capturing transition dynamics across diverse flow conditions. The framework uses an Ensemble Kalman Filter to infer key model parameters, such as near-wall vortex scale and transition center, from limited experimental heat flux data, achieving prediction errors less than 6% for transition onset and peak heat flux. A hybrid feature selection strategy combines global flow parameters and local flow features to train a Hyper-Deep Neural Network, enabling accurate generalization across various scenarios. Furthermore, scaling laws for those model parameters are derived, converting the machine-learning model from the “black-box” to a “white-box” system with clear physical interpretability. The model provides unified predictions of the entire transition process, including transition onset location, peak heat flux, and fully developed turbulent state, outperforming traditional approaches like the C–γ–Reθ model. This work establishes a data-driven turbulence modeling paradigm—physics-guided ML—to reveal universal laws and facilitate the advancement of reliable HTrBL applications.