Global sensitivity metrics from active subspaces with applications

Predictions from science and engineering models depend on input parameters. Global sensitivity metrics quantify the importance of input parameters, which can lead to model insight and reduced computational cost. 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. We develop global sensitivity metrics called activity scores from the estimated active subspace and analytically compare the active subspace-based metrics to established sensitivity metrics. These commonly used metrics include Sobol' indices derived from a variance-based decomposition and derivative-based metrics. Additionally, we outline practical computational methods to estimate the activity scores. We then consider three numerical examples with algebraic scalar valued functions from engineering and biological models. In each case, the models admit reduced dimensional active subspaces. For each of the models, a variety of sensitivity metrics are compared to the activity scores.