Design and analysis of computer experiments with both numeral and distribution inputs

TL;DR

This paper develops new design and analysis methods for computer experiments involving both numerical and distribution inputs, using Wasserstein distance to create space-filling designs and Gaussian process models, demonstrated through simulations and real-world applications.

Contribution

It introduces a novel framework combining Wasserstein distance with Gaussian process modeling for mixed-input computer experiments, including optimal Latin hypercube designs.

Findings

Effective Wasserstein distance-based design criteria

Successful application to metro simulation data

Improved modeling of complex uncertain systems

Abstract

Nowadays stochastic computer simulations with both numeral and distribution inputs are widely used to mimic complex systems which contain a great deal of uncertainty. This paper studies the design and analysis issues of such computer experiments. First, we provide preliminary results concerning the Wasserstein distance in probability measure spaces. To handle the product space of the Euclidean space and the probability measure space, we prove that, through the mapping from a point in the Euclidean space to the mass probability measure at this point, the Euclidean space can be isomorphic to the subset of the probability measure space, which consists of all the mass measures, with respect to the Wasserstein distance. Therefore, the product space can be viewed as a product probability measure space. We derive formulas of the Wasserstein distance between two components of this product probability measure space. Second, we use the above results to construct Wasserstein distance-based space-filling criteria in the product space of the Euclidean space and the probability measure space. A class of optimal Latin hypercube-type designs in this product space are proposed. Third, we present a Wasserstein distance-based Gaussian process model to analyze data from computer experiments with both numeral and distribution inputs. Numerical examples and real applications to a metro simulation are presented to show the effectiveness of our methods.