Fold-Reconstructed Sensitivity Priors and Structure-Preserving BP Neural Curves for Ducted Propeller Hydrodynamic Prediction

Rapid surrogate prediction of ducted propeller performance is challenging when only a limited number of independent geometries are available and operating points belonging to the same geometry are strongly correlated. This study proposes a sensitivity-informed physics-regularized backpropagation neural network (SIPR-BP) for simultaneous prediction of the thrust coefficient KT and the scaled torque coefficient 10KQ. A CFD database comprising 20 Ka4-70-derived parameterized geometries, each evaluated at five advance ratios, provides 100 observations and 20 complete performance curves. The framework combines three main strategies. First, two-component multi-output partial least-squares (PLS) curve surrogates are reconstructed exclusively from the training geometries of each outer fold to generate leakage-controlled conditional Sobol gate priors. Second, the operating coordinate J is separated from geometric gating and represented by five ordered curve nodes, which guarantee non-increasing KT and 10KQ responses over the investigated interval. Third, training-only physics-consistency reliability weighting and a three-member ensemble improve robustness to locally irregular CFD responses and initialization variability. Under a ten-round geometry-grouped holdout protocol, SIPR-BP achieves a geometry-balanced MAPE of 2.65%, RMSE of 0.0112, MAE of 0.00911, and pooled R2 of 0.951. When evaluated under the same outer partitions, a two-component PLS baseline yields a MAPE of 4.38%. Across the evaluated PLS, Extra Trees, GPR, and SVR baselines, SIPR-BP reduces geometry-balanced MAPE by approximately 39.6–79.2%. The results indicate that the proposed framework improves unseen-geometry prediction while preserving the prescribed response-curve structure.