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

TL;DR

This paper introduces a novel framework for designing and analyzing computer experiments involving both functional and scalar inputs, utilizing a norm-based approach and B-splines for computational efficiency.

Contribution

It proposes a two-stage design method for mixed inputs and integrates functional inputs into kriging models using norms and B-splines.

Findings

Generalizes Latin hypercube designs for mixed inputs

Incorporates functional inputs into GP models effectively

Uses B-splines to reduce computational complexity

Abstract

A framework for designing and analyzing computer experiments is presented, which is constructed for dealing with functional and real number inputs and real number outputs. For designing experiments with both functional and real number inputs a two stage approach is suggested. The first stage consists of constructing a candidate set for each functional input and during the second stage an optimal combination of the found candidate sets and a Latin hypercube for the real number inputs is searched for. The resulting designs can be considered to be generalizations of Latin hypercubes. GP 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. In order to make the calculation of these norms computationally feasible, the use of B-splines is promoted.