Bayesian Optimization in Reduced Eigenbases

Parametric shape optimization aims at minimizing a function f ( x ) where x ∈ X ⊂ R d is a vector of d Computer Aided Design parameters, representing diverse characteristics of the shape Ω x . It is common for d to be large, d > 50 , making the optimization diffcult, especially when f is an expensive black-box and the use of surrogate-based approaches [1] is mandatory. Most often, the set of considered CAD shapes resides in a manifold of lower dimension where it is preferable to p erform the optimization. We uncover it through the Principal Comp onent Analysis of a dataset of n designs, mapped to a high-dimensional shape space via ...