  An adaptation of Response Surface Methodology (RSM) when the covariate is of
high or infinite dimensional is proposed, providing a tool for black-box
optimization in this context. We combine dimension reduction techniques with
classical multivariate Design of Experiments (DoE). We propose a method to
generate experimental designs and extend usual properties (orthogonality,
rotatability,...) of multivariate designs to general high or infinite
dimensional contexts. Different dimension reduction basis are considered
(including data-driven basis). The methodology is illustrated on simulated
functional data and we discuss the choice of the different parameters, in
particular the dimension of the approximation space. The method is finally
applied to a problem of nuclear safety.
