In industrial design workflows, it is common that producing new optimized geometries is slow and costly, while assessing a given geometry under many operating conditions through simulation is comparatively affordable. This creates a recurrent bottleneck: engineers can generate many simulation results per design, yet only a limited number of distinct designs are available to support fast exploration and informed decision-making across the design space. Our work is motivated by the need to turn these scarce, high-value design samples into a practical capability for rapid prediction and screening of new candidate designs. To address this gap, we develop a workflow that delivers fast parametric predictions for previously unseen designs while keeping the number of high-fidelity runs per geometry bounded. For each available design, we build a parametric model using sPGD, and then link these per-design parametric models into a global predictor by learning the mapping from design descriptors to parametric response representations using neural networks. Directly aligned with the scarcity of designs, we leverage design sensitivities to increase the effective information content of each geometry: sensitivities are used as an additional learning signal to better transfer trends across designs. When no unified parametrization is available, we introduce an independent representation by embedding each design as a level-set field on a fixed background mesh, enabling consistent simulations and sensitivity computations with finite-element solvers based on the Fictitious Domain formulation. The level-set fields are defined to preserve computational efficiency and to facilitate inference for unseen designs. Initial results on simple case studies are promising in both regimes — shared a priori parametrizations and designs with unknown parametrization — highlighting the potential of the methodology as a practical route to rapid parametric evaluation for new designs under scarce design data.