JMP Blog

Victor_G · Oct 27, 2025 10:05 AM

Introduction

Welcome to the first part of our three-part blog series exploring space filling designs of experiments (DOE). In an era where machine learning, computational experimentation, and simulation play increasingly critical roles in research and development, traditional experimental design approaches sometimes fall short of efficiently exploring complex and continuous factor spaces. This is where space filling designs shine.

What are space filling designs?

Space filling designs are a type of model-agnostic design of experiments (DOE) that aim to uniformly distribute design points throughout the experimental region, maximizing the distance between any two points and the coverage of the design space with a limited number of runs. The analysis of the results often implies the use of simple machine learning models (such as Gaussian process, support vector machine and random forests) that are able to model and approximate complex and non-linear responses.

Space filling designs are originally used for numerical experiments, in domains where the experiments are impossible, complex, expensive, and/or time-consuming. Therefore, phenomena are often studied using numerical simulations, but the calculation time can be very long because of the increasing complexity and precision of models. To avoid running random simulations and enable good coverage of the simulation space, space filling designs are used to spread the computer runs evenly throughout the space studied. Space filling designs typically include no replicates, since numerical simulations are deterministic and produce identical outputs for identical inputs, eliminating the need for repeated runs to estimate variability. Space filling designs are found in various industries, such as the oil, astronomy, optics, nuclear, etc.

Thanks to space filling designs and machine learning models, a precise approximation of the simulation models (called a “surrogate model” or metamodeling) can be done quickly. Surrogate models are used to represent and approximate the results for complex simulation models and, compared to such models, are simpler, compact, and typically less computationally expensive. Since surrogate models approximate the behavior of more complex system, they enable exploring the design space of a complex system, gaining insights into it, optimizing it, and running validation simulations in much less time.

Key characteristics

Space filling designs offer key characteristics regarding the repartition of points and their intended use:

Uniform distribution of points across the design space.
No assumption about the underlying model form.
Well-suited for predictive purposes in low-noise experiments and computer experiments.
Optimal for complex, nonlinear responses.

Why choose space filling designs over classical DOE?

Figure 1: Design of Experiments approaches

Traditional DOE limitations

Assumes specific model terms (main effects, interactions, quadratic effects, etc.).
May leave large regions of design space unexplored.
Optimized for specific statistical objectives (screening and quantitative analysis through effects estimation, polynomial response surface model prediction).

Space filling advantages

Model-independent exploration.
Better global understanding and prediction of complex response behavior.
Ideal for computer simulations, metamodeling and predictive modeling (machine learning).

However space filling designs often require a higher number of points compared to model-based DOE in order to obtain a relevant and predictive model.

Overview of common types of space filling designs

The Space Filling Design platform provides multiple design types for different situations with various factor types. For continuous factors, space filling designs have two objectives:

Maximize the distance between any two design points.
Space the points uniformly.

Space filling designs can be found in JMP at DOE>Special Purpose>Space Filling Design (Figure 2).

Figure 2: Space Filling Design menu

Space filling designs options include Sphere Packing, Latin Hypercube, Uniform, Minimum Potential, Maximum Entropy, Gaussian Process IMSE Optimal, and Fast Flexible Filling.

Designs	Uniform	Sphere Packing (Maximin)	Latin Hypercube	Fast Flexible Filling
Strengths	Excellent space coverage, mathematically optimal uniformity	Optimal point separation	Good one-dimensional projections, easy to generate	Balance between space coverage and projection properties
Weaknesses	Time to compute	Poor projection properties	No constraints handling	Compromise between space coverage and projection properties
Best for	Precise space exploration	Continuous factor spaces with noisy responses	Initial screening, computer experiments	Mixed factor types, balanced exploration, handling of constraints
Type of factors	Only continuous numeric factors	Only continuous numeric factors	Only continuous numeric factors	Continuous and discrete numeric, categorical and mixture factors

To assess how well design points achieve homogeneous coverage of the parameter space, the discrepancy metric compares their distribution against a theoretical uniform distribution.

What is a uniform distribution?

A uniform distribution means equal probability across all possible values within a given range.

In a uniform distribution between 0 and 1, every value has exactly the same likelihood of occurring: there are no preferred regions or clusters. Graphically, this appears as a flat, rectangular shape where the probability density remains constant (Figure 3).

Figure 3: Random uniform distribution generated with 1000 points

The greater the number of points, the easier it is to approximate a uniform distribution.

For space filling designs, uniform distribution ensures points are placed with equal spacing throughout the entire parameter space. This prevents clustering in certain regions while leaving others unexplored, maximizing information coverage with minimal computational runs. The use of this distribution ensures unbiased sampling: each location in the design space has an equal chance of being selected, leading to systematic and efficient exploration of the problem domain.

Common types of space filling designs

Uniform designs

Principle: The basic principle is to create a design, where each factor’s distribution of points follows a uniform distribution as closely as possible. It creates a design that minimizes the difference between the design points (which have an empirical uniform distribution) and a theoretical uniform distribution. This difference between design and theoretical uniform distributions is called discrepancy.

Strengths: Excellent space coverage, mathematically optimal uniformity.
Weakness: Time to compute.
Best for: Precise space exploration.

Figure 4: Representation of uniform design for two factors with 20 runs.
Note how the repartition of points creates a uniform distribution of points for each factor.

Figure 5: Design diagnostic of uniform design.
The minimum distance between two neighboring points is heterogeneous. Discrepancy is low and MaxPro (maximum projection) metric is high with this design.

Sphere packing designs (also called maximin designs)

Principle: It creates a design that maximizes the minimum distance between pairs of design points. The effect of this maximization is to spread the points out as much as possible inside the design region. As a visual explanation, this represents the problem of stacking spheres with the same volume inside a specified volume with the most efficiency.

Strength: Optimal point separation.
Weakness: Poor projection properties.
Best for: Continuous factor spaces with noisy response.

Figure 6: Representation of sphere packing design for two factors with 20 runs.
Note how the repartition of points spreads out design points with a constant distance between neighboring ones.

Figure 7: Design diagnostic of sphere packing design.
The minimum distance between two neighboring points is maximized and similar. No MaxPro metric assessment is available with this design, because points can have identical values for one dimension.

Latin hypercube designs (LHD)

Principle: The basic principle is to create a number of bins equal to the number of runs and ensure that each design point belongs to only one bin for each factor. As many combinations could provide this generation, another criterion (MaxPro) is enforced to make sure repartition of points does not create correlations between factors and to ensure good projection properties. It creates a design that maximizes the minimum distance between design points but requires even spacing of the levels of each factor. Each factor has as many levels as there are runs in the design. This method produces designs that mimic the uniform distribution. The LHD method is a compromise between the sphere packing method and the uniform design method.

Strengths: Good one-dimensional projections, easy to generate.
Weakness: None.
Best for: Initial screening, computer experiments.

Figure 8: Representation of Latin hypercube design for two factors with 20 runs.
Note how the repartition of points creates 20 equidistant bins, approximating a uniform distribution of points for each factor.

Figure 9: Design diagnostic of Latin hypercube design.
The minimum distance between two neighboring points is similar. Discrepancy is low and MaxPro metric is high with this design.

Fast flexible filling designs

Principle: It creates a design using the fast flexible filling (FFF) algorithm. The algorithm begins by generating a large number of random points within the specified design region. These points are then clustered using a fast Ward’s algorithm into a number of clusters that equals the number of runs that you specified. The final design points can be obtained by using the default MaxPro optimality criterion or by selecting the centroid criterion.

Strength: Balance between space coverage and projection properties.
Weakness: Compromise between space coverage and projection properties.
Best for: Mixed factor types, balanced exploration, handling of constraints.

Does it sound complex ? Fear not, a step-by-step walkthrough of the FFF algorithm is presented later!

Figure 10: Representation of fast flexible filling design for two factors with 20 runs.

Figure 11: Design diagnostic of fast flexible filling design.
The minimum distance between two neighboring points is heterogeneous. MaxPro metric assessment is quite high with this design.

BONUS: Fast flexible filling algorithm walkthrough

In this section, we reproduce the steps of the fast flexible filling algorithm to better understand its mechanisms.

Creating columns for factors: In this example, we create two columns for the two continuous factors, each with 100,000 rows and a random uniform formula distribution (Figure 12).

Figure 12: Creation of the factors columns.

The design space should be entirely covered by the random uniform points created with the formula (Figure 13).

Figure 13: Design space covered by 100,000 random uniform points.

Clustering: In Analyze>Clustering, we choose the Hierarchical Cluster platform, specify the two factors X1 and X2 in Y, and select Fast Ward as the method (Figure 14).

Figure 14: Hierarchical cluster launch window

In the red triangle next to Hierarchical Clustering, click on Number of Clusters and specify 20 (20 is the number of points recommended by JMP for any space filling designs with two continuous numeric factors). Then, in the same red triangle, after choosing Save Cluster Means (Figure 15), a new table appears with the 20 clusters means.

Figure 15: Hierarchical clustering option for saving cluster means.

We can also save the clusters in our original table and add the cluster means rows from Cluster Means table. We can then visualize our design space divided by clusters (Figure 16).

Figure 16: Design space divided by 20 clusters.

Filtering: Next, filter out random points and only keep cluster mean points. Our fast flexible filling design (with centroïd criterion) is finished!

We can then compare the design generation following these steps with the result we would obtain by directly generating a 20-run fast flexible filling design with centroïd criterion (Figure 17).

Figure 17: Comparison of the Fast flexible filling designs manually created with the workflow (left) and the one created by JMP with centroïd criterion (right).

The two designs look very similar !

A fast flexible filling design with default MaxPro criterion could be created using the same workflow, but the selection of the representative cluster points won’t be the mean of the clusters; they would be points belonging to each cluster and maximizing the MaxPro criterion: Fast flexible filling design details

Design selection criteria

When choosing between space filling designs, consider:

Objective: Depending on the objective (screening, exploration, precise predictive modeling, etc.) and geometrical/distributional generation emphasis, some designs may be preferred.
Design space dimensionality: The generation of some space filling designs (like uniform designs) may require high computational time for high dimensions.
Factor types: If you have only continuous factors, you can choose an appropriate design based on your objective and dimensionality. When using other type(s) of factors (discrete numeric, categorical, mixture, etc.), your only choice will be to use a fast flexible filling design.
Response characteristics and integration with modeling approaches: Depending on the expected noise in the response, as well as the modeling approaches used (Gaussian process, SVM, tree-based models, etc.), different design configurations may be adapted.
Number of available runs: Depending on the objective, responses to analyze, and available experimental budget, you might choose a design that aligns with your constraints. For example, if you want to homogeneously explore an experimental space in high dimensions using only continuous factors and with a possible noisy response, a sphere packing (maximin) design may be a good option.
Computational complexity of design generation: Depending on the number of runs and dimensionality, you might choose a design with lower generation complexity. Uniform and sphere packing designs are generally more complex to generate than fast flexible filling and Latin hypercube designs.
Augmentation strategies for sequential experimentation: Any design augmentation using a space filling approach will be done using the fast flexible filling methodology.

Coming next

In our next post, we establish the framework for comparing these space filling designs. We define specific responses, factors, and evaluation metrics to systematically assess the performance of different space filling approaches across various scenarios.

This is the first of a three part series on space filling designs of experiments:

Introduction to common types of space filling designs (this post)
Comparative framework and evaluation metrics (coming soon)
Results, analysis and design selection guidelines (coming soon)