A flow-field latent-space framework for surface aerodynamic-load distribution modeling in steady supersonic flows

Accurate prediction of surface aerodynamic load distributions is important for rapid aerodynamic analysis and design under supersonic conditions, where shock waves, expansion waves, and boundary-layer interactions produce strong nonlinearities and sharp local gradients. Conventional direct surrogates may inadequately represent the internal flow evolution governing distributed surface responses. This study proposes a flow-field latent-space (FFLS) framework for modeling distributed surface loads in steady supersonic flows. Instead of mapping operating conditions directly to surface responses, the framework compresses high-dimensional flow-field data into a compact latent representation using a convolutional autoencoder. A latent-space surrogate infers this representation from operating conditions, and a load-prediction model combines the predicted representation with those conditions to estimate surface pressure, wall shear stress, density, and temperature distributions. Numerical experiments use 1000 steady RANS simulations of a two-dimensional diamond airfoil over angles of attack of 0°–30°, Mach numbers of 2–5, and altitudes of 11–20 km, with a fixed 700/300 training-test split. The learned latent variables preserve the main flow structures and provide an effective intermediate representation for load prediction. On the held-out 300-case test set, FFLS reduces the averaged RMSE by 59.07 % relative to direct load mapping and by 46.75 % relative to POD-based load mapping, with corresponding better-case ratios of 98.67 % and 90.00 %. The improvement is concentrated in pressure, density, and temperature, whereas direct load mapping remains slightly more accurate for wall shear stress. A 61-case out-of-distribution evaluation shows region-dependent performance: FFLS remains more accurate than POD-based load mapping on average but does not outperform direct load mapping overall.