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In the reduced order modeling (ROM) framework, the solution of a parametricpartial differential equation is approximated by combining the high-fidelitysolutions of the problem at hand for several properly chosen configurations.Examples of the ROM application, in the naval field, can be found in [31, 24].Mandatory ingredient for the ROM methods is the relation between thehigh-fidelity solutions and the parameters. Dealing with geometricalparameters, especially in the industrial context, this relation may be unknownand not trivial (simulations over hand morphed geometries) or very complex(high number of parameters or many nested morphing techniques). To overcomethese scenarios, we propose in this contribution an efficient and completedata-driven framework involving ROM techniques for shape design andoptimization, extending the pipeline presented in [7]. By applying the singularvalue decomposition (SVD) to the points coordinates defining the hull geometry- assuming the topology is inaltered by the deformation -, we are able tocompute the optimal space which the deformed geometries belong to, hence usingthe modal coefficients as the new parameters we can reconstruct the parametricformulation of the domain. Finally the output of interest is approximated usingthe proper orthogonal decomposition with interpolation technique. To conclude,we apply this framework to a naval shape design problem where the bulbous bowis morphed to reduce the total resistance of the ship advancing in calm water.

A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems