Sensitivity Analysis of High-Dimensional Models with Correlated Inputs
This addresses a critical limitation in sensitivity analysis for computational science applications where inputs are correlated, though it is incremental as it builds on existing methods.
The study tackled the problem of sensitivity analysis for high-dimensional models with correlated inputs, which existing methods assume are independent, by proposing an approach using polynomial chaos expansion and transformations to account for dependencies. The results showed that correlations can invert the sign of sensitivity indices, significantly altering model behavior compared to ignoring correlations.
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.