Computation of Sobol indices in global sensitivity analysis from small data sets by probabilistic learning on manifolds

• Published in: International Journal for Uncertainty Quantification
• Main Authors: Arnst, Maarten, Soize, Christian, Bulthuis, Kevin
• Other Authors: Université de Liège, Laboratoire Modélisation et Simulation Multi-Echelle (MSME), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, Partial financial support by Fund for ScientificResearch (F.R.S.-FNRS) under Grant No. 2.5020.11 and by the Walloon Region
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2021
• Subjects: global sensitivity analysis; Sobol index; probabilistic learning on manifolds; small data; [STAT.ML]Statistics [stat]/Machine Learning [stat.ML]; [MATH.MATH-PR]Mathematics [math]/Probability [math.PR]; [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]; Antarctic; The Antarctic; Antarc*; Ice Sheet
• Online Access: https://hal-upec-upem.archives-ouvertes.fr/hal-02918215; https://hal-upec-upem.archives-ouvertes.fr/hal-02918215/document; https://hal-upec-upem.archives-ouvertes.fr/hal-02918215/file/publi-2020-IJUQ-%28%291-26-arnst-soize-bulthies-preprint.pdf; https://doi.org/10.1615/Int.J.UncertaintyQuantification.2020032674

International audience Global sensitivity analysis provides insight into how sources of uncertainty contribute to uncertainty in predictions of computational models. Global sensitivity indices, also called variance-based sensitivity indices and Sobol indices, are most often computed with Monte Carlo methods. However, when the computational model is computationally expensive and only a small number of samples can be generated, that is, in so-called small-data settings, usual Monte Carlo estimates may lack sufficient accuracy. As a means of improving accuracy in such small-data settings, we explore the use of probabilistic learning. The objective of the probabilistic learning is to learn from the available samples a probabilistic model that can be used to generate additional samples, from which Monte Carlo estimates of the global sensitivity indices are then deduced. We demonstrate the interest of such a probabilistic learning method by applying it in an illustration concerned with forecasting the contribution of the Antarctic ice sheet to sea-level rise.