Benchmarking Active Subspace methods of global sensitivity analysis against variance-based Sobol' and Morris methods with established test functions

Abstract

Active Subspaces is a recently developed concept that identifies essential directions of the response surface of a model, providing sensitivity metrics known as activity scores. We compare activity scoring with the Sobol' and the Morris global methods using a series of well-known benchmark test functions with exactly computable sensitivities. In the ranking context, we analyse the accuracy, efficiency, impact of sampling method, convergence rate, and confidence interval estimation through both bootstrapping and replication. Heat maps that show both numerical rankings and underlying sensitivities with increasing sample size are introduced as a key visualization tool for such analysis. Convergence is also assessed through four previous measures. Activity scores match the total-effect sensitivity index of Sobol' and the absolute mean of elementary effect of Morris in most test cases. Activity scoring can be more computationally efficient. Its potential can be enhanced by expanding methods for approximating the gradient of the model function.