Publication date: 11/10/2021

Space-filling designs are useful for modeling systems that are deterministic or near-deterministic. One example of a deterministic system is a computer simulation. Such simulations can be very complex involving many variables with complicated interrelationships. A goal of designed experiments on these systems is to find a simpler empirical model that adequately predicts the behavior of the system over limited ranges of the factors.

In experiments on systems where there is substantial random noise, the goal is to minimize the variance of prediction. In experiments on deterministic systems, there is no variance but there is bias. Bias is the difference between the approximation model and the true mathematical function. The goal of space-filling designs is to bound the bias.

One approach to bound the bias is to spread the design points out as far from each other as possible while staying inside the experimental boundaries. The other approach is to space the points out evenly over the region of interest.

The Space Filling designer supports the following design methods:

Sphere Packing

Maximizes the minimum distance between pairs of design points. See Sphere-Packing Designs and Create the Sphere-Packing Design for the Borehole Data.

Latin Hypercube

Maximizes the minimum distance between design points but requires even spacing of the levels of each factor. This method produces designs that mimic the uniform distribution. The Latin Hypercube method is a compromise between the Sphere-Packing method and the Uniform design method. See Latin Hypercube Designs.

Uniform

Minimizes the discrepancy between the design points (which have an empirical uniform distribution) and a theoretical uniform distribution. See Uniform Designs.

Minimum Potential

Spreads points out inside a sphere around the center. See Minimum Potential Designs.

Maximum Entropy

Measures the amount of information contained in the distribution of a set of data. See Maximum Entropy Designs.

Gaussian Process IMSE Optimal

Creates a design that minimizes the integrated mean squared error of the Gaussian process over the experimental region. See Gaussian Process IMSE Optimal Designs.

Fast Flexible Filling

The Fast Flexible Filling method forms clusters from random points in the design space. These clusters are used to choose design points according to an optimization criterion. This is the only method that can accommodate categorical factors and constraints on the design space. You can specify linear constraints and disallowed combinations. See Fast Flexible Filling Designs and Creating and Viewing a Constrained Fast Flexible Filling Design.

Note: If the number of runs is 500 or less, a Gaussian Process model is saved to the data table. If the number of runs exceeds 500, a Neural model is saved to the data table.

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