  The global sensitivity analysis of time-dependent processes requires
history-aware approaches. We develop for that purpose a variance-based method
that leverages the correlation structure of the problems under study and
employs surrogate models to accelerate the computations. The errors resulting
from fixing unimportant uncertain parameters to their nominal values are
analyzed through a priori estimates. We illustrate our approach on a harmonic
oscillator example and on a nonlinear dynamic cholera model.
