CFD-validated deep active subspace learning for reliable offline transonic airfoil optimization and shock-control analysis

Offline aerodynamic optimization can fail when a search exploits surrogate error and predicted gains disappear under high-fidelity computational fluid dynamics (CFD) reevaluation. We develop a data-driven deep active subspace method (DASM) that jointly learns nonlinear active coordinates and a neural response for direct reduced-space optimization. Projection-sensitive benchmarks and the Royal Aircraft Establishment 2822 airfoil test the method in an 18-dimensional Class-Shape Transformation space. Controls comprise free- and fixed-θ Kriging, active subspace method (ASM)-Kriging, an artificial neural network (ANN), a Kolmogorov–Arnold network (KAN), and long short-term memory (LSTM). All models use the same fixed CFD information and prespecified, dimension-adapted search settings. Paired validation shows significantly smaller errors for the three-dimensional (3D) and six-dimensional (6D) DASM models than for Kriging, ASM-Kriging, ANN, and KAN. More importantly, pathwise CFD audits give median prediction-to-CFD discrepancies of 1.90% and 7.50% for 3D and 6D DASM. The corresponding discrepancies reach 46.61% for free-θ Kriging, 36.09% for ANN, 35.32% for KAN, and 12.63% for LSTM. The 3D DASM design combines an 18.2% CFD-validated drag reduction with the smallest terminal discrepancy, 1.9%. At nearly equal lift, it also produces lower drag than KAN. The 6D design gives the lowest CFD drag while retaining higher lift and a smaller discrepancy than LSTM. Geometry and flow-field comparisons link these outcomes to smooth reduced-space reconstruction and coordinated redistribution of the transonic compression system. By confining the search to response-informed coordinates, DASM converts surrogate convergence into reliable CFD improvement without adaptive enrichment.