Discontinuity-aware autoencoder for dimensionality reduction of shock-dominated supersonic flows

Supersonic flows are characterized by strong non-stationarity and discontinuity arising from the coexistence of turbulent fluctuations and shock waves. Classical dimensionality reduction approaches exhibit inherent limitations in this regime. Linear methods such as proper orthogonal decomposition (POD) are constrained by the Kolmogorov barrier, while nonlinear autoencoder (AEs)-based manifolds (e.g., multilayer perceptron, MLP, and Kolmogorov–Arnold networks, KAN) rely on inherently smooth representations and, therefore, struggle to accurately resolve discontinuities. To address these challenges, a discontinuity-aware autoencoder (DAE) is proposed to better extract low-dimensional representations of shock-dominated flows. The method extends the KAN-based AE by incorporating learnable non-smooth basis functions into the spline-based activation functions, enabling the unified representation of both smooth and discontinuous flow features. The proposed approach is evaluated on the shock-dominated Burgers' equation, a supersonic square cylinder wake, and flow past cylinder arrays involving strong shock–shock and shock–vortex interactions. The results demonstrate that the DAE consistently outperforms POD, MLP-based, and KAN-based AEs in reconstruction accuracy while requiring fewer modes and parameters. This improvement is attributed to the ability of DAE to explicitly capture discontinuous features and preserve sharp gradients without Gibbs-type oscillations. These findings suggest that incorporating discontinuity-aware representations is essential for efficient dimensionality reduction and reduced-order modeling of shock-dominated systems and provide a physically consistent framework for data-driven modeling of compressible flows.