Quantifying transition predictability: Statistical mapping from initial disturbances to transition onset

Laminar–turbulent transition in boundary layers remains a fundamental challenge, governed by the interplay between external disturbances and nonlinear interactions of perturbations. Quantitative links between similar disturbances and similar transition positions, however, remain elusive. A data-driven framework is proposed to connect the initial disturbance characteristics with transition behavior and to identify the universal features underlying the transition process. Large-scale datasets of flat-plate boundary-layer transition (K-type and H-type) were generated using the nonlinear parabolized stability equations. K-means clustering quantified correlations between initial conditions [frequency, spanwise wavenumber, and two-dimensional (2D)/three-dimensional (3D) amplitudes] and transition onset, defined by the rise in the skin-friction coefficient Cf. A modified Residual Network (ResNet) 18, trained with clustering-derived pseudo-labels, combined with Gradient-weighted Class Activation Mapping, identified transition-relevant features. The results show that similar initial conditions yield clustered transition locations (Pearson correlation coefficient r=0.834; maximum entropy 1.062), indicating strong predictability, while dissimilar conditions may lead to similar transitions (r=0.019), revealing a many-to-one mapping. K-type and H-type transitions share core dynamics, including 2D Tollmien–Schlichting waves, Λ-vortices, and spanwise periodicity. The Convolutional Neural Network achieved 97% validation accuracy. This study establishes bidirectional correlations between initial disturbances and transition responses, and reveals universal structural features of the transition, offering a quantitative foundation for data-driven prediction and control of boundary-layer transition.