Physics-informed multiscale attention wavelet neural operator: A novel framework for instability-wave prediction in hypersonic boundary layers

Accurate prediction of boundary layer transition in hypersonic flows is a critical challenge due to the coexistence of multiple instability mechanisms and their sensitivity to flow conditions. In this work, we propose a physics-informed multiscale attention wavelet neural operator (PIMAWNO) as a surrogate for the linear parabolized stability equations (LPSEs). The method employs a dual-operator collaborative training strategy, in which a perturbation profile operator and a streamwise wavenumber operator are trained on a high-fidelity database while exchanging information through physical normalization conditions. Symlet-9 wavelets are identified as the optimal basis, offering the lowest mean square error across training and testing datasets, with error levels consistently one to two orders of magnitude smaller than perturbation amplitudes. Model performance is evaluated on four canonical instabilities: traveling Mack mode, second mode, cross-flow mode, and centrifugal mode, with perturbation profiles and N-factor curves. Across all cases, PIMAWNO predictions closely reproduce LPSE solutions, accurately capturing both the spatial distribution and downstream amplification of disturbances. Absolute error analysis reveals that discrepancies are concentrated in regions of steep gradients, such as near-wall temperature peaks in the Second mode or spanwise velocity growth in the Centrifugal mode. These results confirm the potential of PIMAWNO as a robust, wavelet-enhanced surrogate model for LPSE, enabling efficient and accurate prediction of hypersonic boundary layer transition and providing a foundation for future stability-based transition prediction strategies.