Physics-Regularized Geometric Manifolds for Efficient Surrogate-Assisted MDO of Tailless BWB UAVs

Multidisciplinary design optimization (MDO) of tailless Blended Wing Body (BWB) Unmanned Aerial Vehicles (UAVs) introduces fundamental geometric and stability challenges: non-linear coupling between reflexed airfoils, spanwise twist, dynamic center-of-gravity (CG) positioning, and design space contamination by unconstrained geometric parameterizations. A 1,000-sample Latin Hypercube ablation study demonstrates that uncoupled chord parameterizations with overlapping exploration bounds waste 35.5% of evaluations on chord-inverted configurations achieving 29% lower maximum L/D without triggering potential-flow solver divergence, thereby contaminating surrogate training with an aerodynamically inferior dead zone. To eliminate this dead zone, a C1-continuous Hermite geometric manifold is formulated that enforces strict chord monotonicity (c_root >= c_blend >= c_tip) for aft-swept BWB planforms, eliminating chord inversions by construction and focusing surrogate training on the physically productive subspace. This manifold is coupled with an automated mass-centroid balance solver that dynamically inverts internal battery placement to achieve robust static margin (SM = 22.5%) and natural pitch trim (C_m = -0.019) at zero elevon deflection. Across a 10,087-evaluation potential-flow campaign, a 5-MLP ensemble surrogate achieves cross-validation R² >= 0.991 across all aerodynamic and stability targets; a Random Forest feasibility gate achieves 92.5% precision, enabling 287 active learning evaluations to deliver a +7.5% (+20.9 km) range increase to 298.7 km (340.7 km under verified 182.5 Wh/kg pack density). Multi-point cross-solver consistency analysis against viscous 3D strip theory (AeroBuildup) demonstrates that the VLM pipeline consistently underpredicts cruise aerodynamic efficiency relative to the higher-fidelity solver (L/D = 17.12 versus 23.22), behaving as a conservative estimator for attached-flow cruise drag within the computational hierarchy employed.