Informational probabilistic sensitivity analysis and active learning surrogate modelling

In this paper, information theory is applied for probabilistic sensitivity analysis and surrogate modelling with active learning. One of the authors has recently proposed the adoption of the informational coefficient of correlation as a measure of dependence between random variables, in place of the largely adopted linear coefficient of correlation. Here, it is shown that the informational coefficient of correlation can be used for probabilistic sensitivity analysis based on the Value of Information (VoI). Effective Informational sensitivity indices based on the mutual information are presented. Moreover, two novel learning functions for adaptive sampling are proposed. The first, called H-function, gives rise to the method AK-H (Adaptive Kriging-Entropy), which describes the epistemic uncertainty through the entropy metric. The second, called MI-function, gives rise to the method AL-MI (Active Learning-Mutual Information), which describes the model error through the Mutual Information. The peculiarity of AL-MI is that it allows the implementation of active learning in any kind of surrogate modelling, even different from Kriging. The two learning functions are applied for two different categories of problems: (i) regression and (ii) evaluation of failure probability within the framework of structural reliability analysis. Numerical examples show its features and its potential for application of the proposed approach.