Sensitivity Prewarping for Local Surrogate Modeling

TL;DR

This paper introduces a method that uses global sensitivity analysis to preprocess inputs through warping, enabling local surrogate models to better capture complex input-output relationships in high-dimensional problems.

Contribution

It proposes a novel input warping technique based on sensitivity analysis to improve local surrogate modeling of complex computer experiments.

Findings

Enhanced surrogate model accuracy on benchmark functions

Effective handling of high-dimensional input spaces

Validated on automotive industry simulator data

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 experiments via local models, which induce sparsity by only considering short range interactions, can tackle huge analyses of complicated input-output relationships. However, 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 information from a global sensitivity analysis into the surrogate model as an input rotation and rescaling preprocessing step. We discuss the relationship between several 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.