Efficient global sensitivity analysis method for dynamic models in high dimensions

Dynamic models generating time-dependent model predictions are typically associated with high-dimensional input spaces and high-dimensional output spaces, in particular if time is discretized. It is computationally prohibitive to apply traditional global sensitivity analysis (SA) separately on each time output, as is common in the literature on multivariate SA. As an alternative, we propose a novel method for efficient global SA of dynamic models with high-dimensional inputs by combining a new polynomial chaos expansion (PCE)-driven partial least squares (PLS) algorithm with the analysis of variance. PLS is used to simultaneously reduce the dimensionality of the input and output variables spaces, by identifying the input and output latent variables that account for most of their joint variability. PCE is incorporated into the PLS algorithm to capture the non-linear behavior of the physical system. We derive the sensitivity indices associated with each output latent variable, based on which we propose generalized sensitivity indices that synthesize the influence of each input on the variance of entire output time series. All sensitivities can be computed analytically by post-processing the coefficients of the PLS-PCE representation. Hence, the computational cost of global SA for dynamic models essentially reduces to the cost for estimating these coefficients. We numerically compare the proposed method with existing methods by several dynamic models with high-dimensional inputs. The results show that the PLS-PCE method can obtain accurate sensitivity indices at low computational cost, even for models with strong interaction among the inputs.