Global sensitivity metrics from active subspaces

TL;DR

This paper introduces activity scores derived from active subspaces to provide global sensitivity metrics, offering insights into important model parameters and computational advantages, validated through numerical examples with engineering models.

Contribution

The paper develops activity scores as a new sensitivity metric from active subspaces, relating them to existing metrics and demonstrating their effectiveness through numerical examples.

Findings

Activity scores align with traditional sensitivity metrics.

Active subspaces reveal low-dimensional structures in models.

Method reduces computational cost for sensitivity analysis.

Abstract

Predictions from science and engineering models depend on several input parameters. Global sensitivity analysis quantifies the importance of each input parameter, which can lead to insight into the model and reduced computational cost; commonly used sensitivity metrics include Sobol' total sensitivity indices and derivative-based global sensitivity measures. 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 active subspace, which yield insight into the important model parameters. We mathematically relate the activity scores to established sensitivity metrics, and we discuss computational methods to estimate the activity scores. We show two numerical examples with algebraic functions taken from simplified engineering models. For each model, we analyze the active subspace and discuss how to exploit the low-dimensional structure. We then show that input rankings produced by the activity scores are consistent with rankings produced by the standard metrics.