Kernel-based sensitivity analysis techniques for uncertainty quantification

Abstract

Sensitivity analysis is a fundamental tool in understanding the behavior of complex systems and models. Several types of Global Sensitivity Analysis (GSA) have been developed, ranging from variance decomposition via the Sobol’ indices to moment-independent techniques, accounting for the shift in the whole shape of the distribution rather than only the variance. Building upon moment-independent techniques, the application of kernels has been widely used for more complex problems with dependent inputs, an area where standard techniques lack. However, one major drawback of kernel-based techniques is the lack of interpretability of the produced results. In the context of this thesis, we investigate a specific kernel based technique, the Hilbert-Schmid Independence Criterion (HSIC), and attempt to produce a set of indices that are easily interpretable by the practitioner. The HSIC methodology, along with our own proposed methodology used to estimate the absolute and relative importance of model inputs, are then applied to a set of problems of increasing complexity.

The resulting indices are interpreted and discussed in order to understand:
• How the scale of the information each input carries affects the output of the model
• The interpretation of the produced sensitivity indices using the HSIC methodology.