Mathematics

 The active subspaces approach represents one of the emerging ideas for dimension reduction in the parameter studies. The concept was introduced by Constantine and employed in different real problems. A characteristic of the active subspaces is that instead of identifying a subset of the inputs as important, they identify a set of important directions in the space of all inputs. If the simulation’s prediction does not change as the inputs move along a particular direction, then we can safely ignore that direction in the parameter study. After identifying an active subspace it is possible to perform different parameter studies such as response surfaces, integration, optimization and statistical inversion. We are going to introduce the Active Subspace Method and to show a test case. Moreover we present an application in naval engineering performing the reduction of the parameters space constructed exploiting the Free Form Deformation of the DTMB 5415 hull.