Sensitivity Prewarping for Local Surrogate Modeling

Nathan Wycoff, Mickael Binois, Robert Gramacy

Abstract:

In the continual effort to improve product quality and decrease operations costs,
computational modeling is increasingly being deployed to determine feasibility of
product designs or configurations. Surrogate modeling of these computer experi-
ments via local models, which induce sparsity by only considering short range inter-
actions, can tackle huge analyses of complicated input-output relationships. How-
ever, narrowing focus to local scale means that global trends must be re-learned
over and over again. In this article, we propose a framework for incorporating in-
formation from a global sensitivity analysis into the surrogate model as an input
rotation and rescaling preprocessing step. We discuss the relationship between sev-
eral sensitivity analysis methods based on kernel regression before describing how
they give rise to a transformation of the input variables. Specifically, we perform
an input warping such that the “warped simulator” is equally sensitive to all input
directions, freeing local models to focus on local dynamics. Numerical experiments
on observational data and benchmark test functions, including a high-dimensional
computer simulator from the automotive industry, provide empirical validation.