  Methodologies for reducing the design-space dimensionality in shape
optimization have been recently developed based on unsupervised machine
learning methods. These methods provide reduced dimensionality representations
of the design space, capable of maintaining a certain degree of the original
design variability. Nevertheless, they usually do not allow to use directly the
original parameterization method, representing a limitation to their widespread
application in the industrial field, where the design parameters often pertain
to well-established parametric models, e.g. CAD (computer-aided design) models.
This work presents how to embed the parametric-model original parameters in a
reduced-dimensionality representation of the design space. The method, which
takes advantage from the definition of a newly-introduced generalized feature
space, is demonstrated, as a proof of concept, for the reparameterization of 2D
Bezier curves and 3D free-form deformation design spaces and the consequent
solution of simulation-driven design optimization problems of a subsonic
airfoil and a naval destroyer in calm water, respectively.
