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      Global sensitivity metrics from active subspaces

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          Abstract

          Predictions from science and engineering models depend on several input parameters. Global sensitivity analysis metrics quantify the importance of each input parameter, which can lead to insight into the model and reduced computational cost; commonly used sensitivity metrics include Sobol' indices derived from a variance-based decomposition and derivative-based metrics. Active subspaces are an emerging set of tools for identifying important directions in a model's input parameter space; these directions can be exploited to reduce the model's dimension enabling otherwise infeasible parameter studies. In this paper, we develop global sensitivity metrics called activity scores from the estimated active subspace, which give insight into the important model parameters. We analytically compare the activity scores to established sensitivity metrics, and we discuss computational methods to estimate the activity scores. We then show two numerical examples with algebraic functions from engineering models. For each case, we demonstrate that the model admits a one-dimensional active subspace. We then compare the standard sensitivity metrics to the activity scores, and we find that all metrics give consistent rankings for the input parameters.

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          Journal
          1510.04361

          Numerical & Computational mathematics
          Numerical & Computational mathematics

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