  We propose a numerical pipeline for shape optimization in naval engineering
involving two different non-intrusive reduced order method (ROM) techniques.
Such methods are proper orthogonal decomposition with interpolation (PODI) and
dynamic mode decomposition (DMD). The ROM proposed will be enhanced by active
subspaces (AS) as a pre-processing tool that reduce the parameter space
dimension and suggest better sampling of the input space. We will focus on
geometrical parameters describing the perturbation of a reference bulbous bow
through the free form deformation (FFD) technique. The ROM are based on a
finite volume method (FV) to simulate the multi-phase incompressible flow
around the deformed hulls. In previous works we studied the reduction of the
parameter space in naval engineering through AS [38, 10] focusing on different
parts of the hull. PODI and DMD have been employed for the study of fast and
reliable shape optimization cycles on a bulbous bow in [9]. The novelty of this
work is the simultaneous reduction of both the input parameter space and the
output fields of interest. In particular AS will be trained computing the total
drag resistance of a hull advancing in calm water and its gradients with
respect to the input parameters. DMD will improve the performance of each
simulation of the campaign using only few snapshots of the solution fields in
order to predict the regime state of the system. Finally PODI will interpolate
the coefficients of the POD decomposition of the output fields for a fast
approximation of all the fields at new untried parameters given by the
optimization algorithm. This will result in a non-intrusive data-driven
numerical optimization pipeline completely independent with respect to the full
order solver used and it can be easily incorporated into existing numerical
pipelines, from the reference CAD to the optimal shape.
