Reduced-order physics-constrained deep learning for shock-dominated supersonic channel flows

A reduced-order physics-constrained deep learning framework, SupersonicNet, is developed for the rapid prediction of two-dimensional supersonic flow fields (Ma 2.5–5.0) in confined channels with variable forward-facing step geometries. The framework is built upon a modified U-Net architecture. The continuity equation and the ideal gas equation of state are embedded as soft constraints in the loss function. The input matrices, consisting of a boundary identifier, a signed distance function for wall geometry, and a pressure boundary condition, mirror the conventional computational fluid dynamics (CFD) solver setup and enable feature learning across diverse geometric configurations. The model accurately predicts flow fields at unseen Mach numbers without additional CFD samples or retraining, capturing Mach number-dependent shock patterns and their interactions with variable step geometries. The reduced-order physics-constraint reduces conservation equation residuals and suppresses nonphysical errors in high-gradient regions such as shock-wave zones. A single flow-field prediction requires 0.1 s on a graphics processing unit (GPU), achieving a speedup of 4.39 × 103 over conventional CFD simulations. This work establishes a multi-channel surrogate modeling framework that integrates physical priors with data-driven learning, delivering a computationally efficient and physically consistent solution for supersonic flow-field prediction.