Global sensitivity analysis; Probabilistic learning on manifolds; Small data; Sobol index; Statistics and Probability; Modeling and Simulation; Discrete Mathematics and Combinatorics; Control and Optimization
Abstract :
[en] 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.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Arnst, Maarten ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational and stochastic modeling
Soize, Christian; Modélisation et Simulation Multi-Echelle, Université Paris-Est Marne-la-Vallée, MSME, UMR 8208, CNRS, Marne-la-Vallée, France
Bulthuis, Kevin ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)
Language :
English
Title :
Computation of sobol indices in global sensitivity analysis from small data sets by probabilistic learning on manifolds
Publication date :
2021
Journal title :
International Journal for Uncertainty Quantification
M. Arnst and C. Soize acknowledge the Fund for Scientific Research (F.R.S.-FNRS) for its financial support for research stays, and K. Bulthuis acknowledges the F.R.S.-FNRS for its financial support for his F.R.S.-FNRS research fellowship. Computational resources have been provided by the Consortium des Équipements de Calcul Intensif (CÉCI), funded by the F.R.S.-FNRS under Grant No. 2.5020.11 and by the Walloon Region.M. Arnst and C. Soize acknowledge the Fund for Scientific Research (F.R.S.-FNRS) for its financial support for research stays, and K. Bulthuis acknowledges the F.R.S.-FNRS for its financial support for his F.R.S.-FNRS research fellowship. Computational resources have been provided by the Consortium des Équipements de Calcul Inten-sif (CÉCI), funded by the F.R.S.-FNRS under Grant No. 2.5020.11 and by the Walloon Region.
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