Bayesian shape optimisation in high dimensional design spaces using isogeometric boundary element analysis

Abstract

In this work, we employ dimensionality reduction and a Bayesian optimisation approach in an isogeometric analysis (IGA) setting to reduce the design space’s dimensionality and ease its exploration while reducing the number of required design evaluations. In the first step, statistical dependencies implicit in the shape modification function encode essential latent features of the underlining shape while maintaining the maximum geometric variance. These latent features are used to form a low-dimensional design subspace with a correspondingly low-dimensional representation of the shape modification function. The subspace is then employed in design optimisation with a Bayesian approach. During space exploration, smooth surface representations are reconstructed from the discrete design instances of the subspace and evaluated with an IGA-enabled hydrodynamic solver. The proposed approach is demonstrated for a design optimisation of a naval ship-hull model, originally parameterised by 27 parameters, aiming at the minimisation of its wave-making resistance. The benefits of the proposed approach are contrasted with conventional optimisation procedures.