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.