  Reducing the dimensionality and uncertainty of design spaces is a key
prerequisite for shape optimisation in computationally intensive fluid
problems. However, running these analyses at an offline stage itself poses a
computationally demanding task. In this work, we propose a unique framework for
the inexpensive implementation of sensitivity analyses for reducing the
dimensionality of the design space in wave-resistance problems. At the heart of
our approach is the formulation of a geometric operator that leverages, via
high-order geometric moments, the underlying connection between geometry and
physics, specifically the wave-resistance coefficient ($C_w$), of ships using
the slender body theory based on the well-known Vossers' integral. The
resulting geometric operator is computationally inexpensive yet
physics-informed and can act as a geometry-based surrogate to drive parametric
sensitivities. To analytically demonstrate the capability of the proposed
approach, we use a well-known benchmark geometry, namely, the modified Wigley
hull. Its simple analytical formulation allows for closed expressions of the
geometric operators and exploration of computational domains that would
otherwise be inaccessible. In this context, the proposed geometric operator
outperforms existing similar approaches by achieving 100% similarity with $C_w$
at a fraction of the computational cost.
