Plans D'Experiences D'Information De Kullback-Leibler Minimale

TL;DR

This paper introduces a novel experimental design method that uses Kullback-Leibler divergence and Shannon entropy estimation to optimize the spread of points in the input space, improving the efficiency of computer simulations.

Contribution

It proposes a new space-filling design approach based on Kullback-Leibler divergence and entropy estimation, enhancing the selection of input points for simulations.

Findings

Effective in spreading points evenly across the experimental region

Reduces the number of simulations needed for accurate modeling

Provides a flexible framework for various model types

Abstract

Experimental designs are tools which can dramatically reduce the number of simulations required by time-consuming computer codes. Because we don't know the true relation between the response and inputs, designs should allow one to fit a variety of models and should provide information about all portions of the experimental region. One strategy for selecting the values of the inputs at which to observe the response is to choose these values so they are spread evenly throughout the experimental region, according to "space-filling designs". In this article, we suggest a new method based on comparing the empirical distribution of the points in a design to the uniform distribution with the Kullback-Leibler information. The considered approach consists in estimating this difference or, reciprocally, the Shannon entropy. The entropy is estimated by a Monte Carlo method where the density function is replaced by its kernel density estimator or by using the nearest neighbor distances