Computer experiments with functional inputs and scalar outputs by a norm-based approach

A framework for designing and analyzing computer experiments is presented, which is constructed for dealing with functional and scalar inputs and scalar outputs. For designing experiments with both functional and scalar inputs, a two-stage approach is suggested. The first stage consists of constructing a candidate set for each functional input. During the second stage, an optimal combination of the found candidate sets and a Latin hypercube for the scalar inputs is sought. The resulting designs can be considered to be generalizations of Latin hypercubes. Gaussian process models are explored as metamodel. The functional inputs are incorporated into the Kriging model by applying norms in order to define distances between two functional inputs. We propose the use of B-splines to make the calculation of these norms computationally feasible.