Sobol’ sensitivity indices– A Machine Learning approach using the Dynamic Adaptive Variances Estimator with Given Data

Abstract

Global sensitivity analysis is today a widely recognized discipline with an extensive application in an increasing number of domains. Today, methodological development and available software, as well as a broader knowledge and debate on the topic, make investigations feasible which were simply impossible or too demanding a few years ago. Among global sensitivity methods, the variance-based techniques and Monte Carlo-based estimators related to Sobol’ sensitivity indices are mostly implemented due to their versatility and easiness of interpretation. Nevertheless, the strict dependency of the analysis cost on the number of the investigated factors and the need of a designed input are still a major issue. A reduction of the required model evaluations can be achieved with the use of quasi-Monte Carlo sequences, the study of groups of inputs, and the sensitivity indices computation through higher performing estimators such as the Innovative Algorithm based on dynamic adaptive variances recently proposed by the authors. However, all these strategies even cutting significantly the necessary model runs are not able to overcome the barrier of a structured input. This paper proposes a machine learning approach that allows us to estimate Sobol’ indices using the outstanding dynamic adaptive variances estimator starting from a set of Monte Carlo given data. Tests have been run on three relevant functions. In most cases, the results are very promising and seem to positively overcome the limit of a design-data approach keeping all the advantages of the Sobol’ Monte Carlo estimator.