Sensitivity Prewarping for Local Surrogate Modeling. (arXiv:2101.06296v1 [stat.ML])

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.



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