Sensitivity Analysis of High-Dimensional Models with Correlated Inputs
Juraj Kardos Wouter Edeling Diana Suleimenova Derek Groen Olaf Schenk
Sensitivity analysis is an important tool used in many domains of
computational science to either gain insight into the mathematical model and
interaction of its parameters or study the uncertainty propagation through the
input-output interactions. In many applications, the inputs are stochastically
dependent, which violates one of the essential assumptions in the
state-of-the-art sensitivity analysis methods. Consequently, the results
obtained ignoring the correlations provide values which do not reflect the true
contributions of the input parameters. This study proposes an approach to
address the parameter correlations using a polynomial chaos expansion method
and Rosenblatt and Cholesky transformations to reflect the parameter
dependencies. Treatment of the correlated variables is discussed in context of
variance and derivative-based sensitivity analysis. We demonstrate that the
sensitivity of the correlated parameters can not only differ in magnitude, but
even the sign of the derivative-based index can be inverted, thus significantly
altering the model behavior compared to the prediction of the analysis
disregarding the correlations. Numerous experiments are conducted using
workflow automation tools within the VECMA toolkit.