Design of Computer Experiments Using Competing Distances Between Set-Valued Inputs
In many numerical simulation experiments from natural sciences and engineering, inputs depart from the classical moderate-dimensional vector set-up and include more complex objects such as parameter fields or maps. In this case, and when inputs are generated using stochastic methods or taken from a pre-existing large set of candidates, one often needs to choose a subset of “representative” elements because of practical restrictions. Here we tackle the design of experiments based on distances or dissimilarity measures between input maps, and more specifically between inputs of set-valued nature. We consider the problem of choosing experiments given dissimilarities such as the Hausdorff or Wasserstein distances but also of eliciting adequate dissimilarities not only based on practitioners’ expertise but also on quantitative and graphical diagnostics including nearest neighbour cross-validation and non-Euclidean structural analysis. The proposed approaches are illustrated on an original uncertainty quantification case study from mechanical engineering, where using partitioning around medoids with ad hoc distances gives promising results in terms of stratified sampling.