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.

翻译：敏感性分析是计算科学多个领域中的重要工具，用于深入了解数学模型及其参数的相互作用，或研究通过输入-输出交互的不确定性传播。在许多应用中，输入具有随机依赖性，这违反了现有敏感性分析方法的基本假设之一。因此，忽略相关性得到的结果所提供的数值未能反映输入参数的真实贡献。本研究提出了一种方法，利用多项式混沌展开法以及Rosenblatt变换和Cholesky变换来处理参数相关性，以体现参数依赖关系。在方差和基于导数的敏感性分析背景下，讨论了相关变量的处理。我们证明，相关参数的敏感性不仅在幅度上可能不同，甚至基于导数的指标的符号也可能反转，从而与忽略相关性的分析预测相比，显著改变模型行为。利用VECMA工具包中的工作流自动化工具进行了大量实验。