Surrogate modeling in engineering design is fundamentally challenged by highly constrained and strongly correlated design spaces, particularly when only a limited number of high-fidelity simulations are available. In such settings, classical regression-based surrogates ignore the intrinsic geometry of the feasible design region, while probabilistic generative models such as variational autoencoders (VAEs) often produce unstable or incoherent samples when data are scarce. This work utilizes the Reduced-Rank Autoencoder (RRAE), a deterministic deep generative model with an explicit SVD-based low-rank latent structure, to learn the intrinsic dimensionality and geometry of feasible design manifolds. By enforcing a shared low-rank representation across the dataset, the RRAE yields structured and interpretable latent embeddings that expose dominant modes of variation and enable direct navigation within the space of valid designs. Unlike conventional VAEs, the RRAE avoids distribution-matching objectives and preserves coherent sampling behavior even in severely data-limited regimes, ensuring that interpolation and exploration remain confined to physically meaningful configurations. The approach is first validated on controlled benchmarks, where RRAE is shown to produce more stable and coherent samples than the VAE when training data are limited. The method is then applied to the AirfRANS airfoil dataset, a representative aerodynamic design benchmark. The learned latent coordinates form a smooth, low-dimensional design manifold that supports physically consistent interpolation and interpretable exploration. These results indicate that RRAE surrogates provide a reliable and practical framework for constrained engineering design and optimization.