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We propose a numerical pipeline for shape optimization in naval engineeringinvolving two different non-intrusive reduced order method (ROM) techniques.Such methods are proper orthogonal decomposition with interpolation (PODI) anddynamic mode decomposition (DMD). The ROM proposed will be enhanced by activesubspaces (AS) as a pre-processing tool that reduce the parameter spacedimension and suggest better sampling of the input space. We will focus ongeometrical parameters describing the perturbation of a reference bulbous bowthrough the free form deformation (FFD) technique. The ROM are based on afinite volume method (FV) to simulate the multi-phase incompressible flowaround the deformed hulls. In previous works we studied the reduction of theparameter space in naval engineering through AS [38, 10] focusing on differentparts of the hull. PODI and DMD have been employed for the study of fast andreliable shape optimization cycles on a bulbous bow in [9]. The novelty of thiswork is the simultaneous reduction of both the input parameter space and theoutput fields of interest. In particular AS will be trained computing the totaldrag resistance of a hull advancing in calm water and its gradients withrespect to the input parameters. DMD will improve the performance of eachsimulation of the campaign using only few snapshots of the solution fields inorder to predict the regime state of the system. Finally PODI will interpolatethe coefficients of the POD decomposition of the output fields for a fastapproximation of all the fields at new untried parameters given by theoptimization algorithm. This will result in a non-intrusive data-drivennumerical optimization pipeline completely independent with respect to the fullorder solver used and it can be easily incorporated into existing numericalpipelines, from the reference CAD to the optimal shape.

Shape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces