A1555
Title: Axis-neighbor geometry and length-scale identifiability in Gaussian process models
Authors: Chenlu Shi - New Jersey Institute of Technology (United States) [presenting]
Lin Wang - Purdue University (United States)
Abstract: In computer experiments, experimental designs for Gaussian process surrogates are often chosen to achieve global space-filling coverage for prediction. However, the same simulator runs must also support estimation of covariance hyperparameters, and designs that are effective for prediction alone may yield weak or unstable length-scale inference, especially for anisotropic GP models. A geometry-driven framework is developed that links experimental design directly to length-scale identifiability in GP models. For general designs, lower bounds are derived for the diagonal Fisher information that depend explicitly on local axis-neighbor geometry through the minimum coordinate-isolating spacing and the multiplicity of closest such pairs. These results show that, in the small-length-scale regime, stable inference is governed by local directional structure rather than by global spread alone. Motivated by this theory, a structured design is proposed that is a strong orthogonal array of strength 2+, and hence combines space-filling properties with a rich collection of short coordinate-isolating pairs. Explicit Fisher-information bounds and sharp small-length-scale asymptotics are further derived for the proposed design, and a structured level-expansion is introduced that refines global resolution while preserving the local geometry responsible for length-scale identifiability. The theoretical findings are further validated through extensive numerical experiments.
