Numerical studies of space filling designs: optimization of Latin Hypercube Samples and subprojection properties

TL;DR

This paper evaluates and optimizes Latin Hypercube Sampling designs for high-dimensional computer experiments, focusing on space filling properties, subprojection robustness, and convergence of optimization algorithms.

Contribution

It introduces new insights into optimizing Latin Hypercube Samples and analyzes their subprojection properties for better high-dimensional space exploration.

Findings

Optimized Latin Hypercube Samples improve space filling in high dimensions.

Certain algorithms show faster convergence and robustness in design optimization.

Deep analysis of 2D-subprojection properties enhances understanding of design quality.

Abstract

Quantitative assessment of the uncertainties tainting the results of computer simulations is nowadays a major topic of interest in both industrial and scientific communities. One of the key issues in such studies is to get information about the output when the numerical simulations are expensive to run. This paper considers the problem of exploring the whole space of variations of the computer model input variables in the context of a large dimensional exploration space. Various properties of space filling designs are justified: interpoint-distance, discrepancy, minimum spanning tree criteria. A specific class of design, the optimized Latin Hypercube Sample, is considered. Several optimization algorithms, coming from the literature, are studied in terms of convergence speed, robustness to subprojection and space filling properties of the resulting design. Some recommendations for building such designs are given. Finally, another contribution of this paper is the deep analysis of the space filling properties of the design 2D-subprojections.