A new criterion based on Kullback-Leibler information for space filling designs

TL;DR

This paper introduces a novel criterion based on Kullback-Leibler information for creating space filling designs, aiming to optimize the distribution of experimental points to improve computer simulation efficiency.

Contribution

It proposes a new design criterion utilizing Kullback-Leibler divergence and Shannon entropy estimation methods for better space filling in experimental designs.

Findings

The criterion effectively spreads points evenly across the experimental region.

It employs Monte Carlo methods with kernel density estimation and nearest neighbor distances.

The approach enhances the quality of experimental designs for computer simulations.

Abstract

Experimental designs are tools which can drastically reduce the number of simulations required by time-consuming computer codes. One strategy for selecting the values of the inputs, whose response is to be observed, is to choose these values so that they are spread evenly throughout the experimental region, according to ?space filling designs?. In this article, we suggest a new criterion based on the Kullback-Leibler information for design construction. The aim is to minimize the difference between the empirical distribution of the design points and the uniform distribution which is equivalent to maximizing the Shannon entropy. The entropy is estimated by a Monte Carlo method, where the density function is replaced with its kernel density estimator or by using the nearest neighbor distances.