In this work we present both industrial and biomedical applications, focusing on shape
parametrization and parameter space reduction by means of active subspaces. In particular
we introduce a combined parameter and model reduction methodology using a POD-Galerkin
approach, and its application to the efficient numerical estimation of a pressure
drop in a set of deformed carotids . The aim is to simulate a wide range of possible
occlusions after the bifurcation of the carotid artery. A parametric description of
the admissible deformations, based on radial basis functions interpolation technique
implemented in the PyGeM python package, is introduced. The use of the reduced order
model acting on the reduced parameter space allows significant computational savings
and better performances. Moreover we present the reduction of heterogeneous parameter
space in a naval engineering problem, that is the hydrodynamic flow past the hull
of a ship advancing in calm water , considering structural and shape parameters.
The geometrical parametrization is done via free form deformation. Some perspectives
on a complete shape optimization pipeline by means of Dynamic Mode Decomposition (DMD)
and POD with interpolation (PODI) are presented , together with the integration
of the python packages PyDMD and EZyRB respectively.