Space-Filling Designs

Space-Filling Designs are experimental designs that distribute design points uniformly throughout the factor space — ensuring that no region is over- or under-sampled, providing good coverage for building surrogate models when the response surface shape is unknown.

Key Space-Filling Designs

• Latin Hypercube Sampling (LHS): Each factor level appears exactly once in each row and column of the design matrix.
• Sobol Sequences: Quasi-random low-discrepancy sequences with proven uniformity properties.
• MaxiMin: Maximizes the minimum distance between any two design points.
• Uniform Design: Distributes points on a uniform grid with good space-filling properties.

Why It Matters

• Model-Free: No assumption about the response shape — good initial designs for unknown processes.
• Surrogate Models: Provide training data for Gaussian processes, neural networks, and other data-driven models.
• Computer Experiments: Standard approach for sampling simulation models (TCAD, process simulation).

Space-Filling Designs are spreading experiments evenly — distributing points uniformly across the parameter space for unbiased exploration.