Do global sensitivity metrics for parameterized dynamical systems admit their own dynamical systems?
Continuous time dynamical systems in applications include input parameters (rate constants, forcings, etc.) that must be set using measurement data. The calibration process introduces error in the fitted parameters. Part of assessing the effects of parameter error on outputs of interest is analysis of the output sensitivity with respect to inputs. Global (as opposed to local, derivative-based) sensitivity metrics are typically formulated for a scalar-valued function of several variables. However, for dynamical systems the outputs also depend on time. We can construct a time series from the global sensitivity metrics at each point in time. Does this time series admit its own separate dynamical system -- perhaps derived from or related to the underlying dynamical system? I’ll describe our initial efforts to model these dynamical systems derived from global sensitivity metric time series, and I’ll discuss several open challenges in both analysis and numerical computation. If we can accurately model these time series with dynamical systems, then we can dramatically reduce the computational cost of global sensitivity analysis for parameterized dynamical systems.