Task-preserving neural segmentation of overlapping shocks and vortex cores in compressible flows

Abstract

Shock fronts and vortex cores often coexist and overlap in compressible flows, where walls, wakes and shear layers also produce strong gradients. Refining a network to detect one structure can therefore degrade its prediction of the other without revealing the loss in the optimized score. We present a task-preserving formulation for simultaneous shock and vortex-core segmentation. The experiments use two solvers and include supersonic diamond-airfoil flows at several incidences and Reynolds numbers, together with circular- and elliptical-cylinder flows. A shared primitive encoder feeds separate shock and vortex decoders with independent sigmoid outputs, allowing the two classes to overlap. Adaptation is confined to the relevant branch: zero-initialized adapters supply rotational diagnostics only to the vortex decoder, while corrected shock supervision updates only the shock decoder. All dependencies of the protected output remain fixed, and bitwise equality is verified on every evaluation field. Compression and conservation-jump (Rankine--Hugoniot) signatures provide weak shock supervision; rotation and topology provide vortex candidates. Analytical oblique-shock rays, Billig's bow-shock correlation and an isentropic vortex supply references independent of these labels. Under the same corrected-target budget, the restricted model and a capacity-matched shared-decoder U-Net obtain comparable shock agreement. Their airfoil vortex-core Dice overlap scores, however, are 0.83 and 0.08, respectively. A soft retention penalty recovers most of the U-Net's lost core agreement. The frozen shock-adapted models locate the tested analytical oblique-shock rays within 0.003 chord. An additional branch identifies expanding-flow regions, which are distinguished from centred Prandtl--Meyer expansion fans through comparison with ideal shock--expansion theory.