Computation of Sobol indices in global sensitivity analysis from small data sets by probabilistic learning on manifolds
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...
Published in: | International Journal for Uncertainty Quantification |
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ftuniveiffel:oai:HAL:hal-02918215v1 2024-04-28T07:57:32+00:00 Computation of Sobol indices in global sensitivity analysis from small data sets by probabilistic learning on manifolds Arnst, Maarten Soize, Christian Bulthuis, Kevin 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 2021 https://hal.science/hal-02918215 https://hal.science/hal-02918215/document https://hal.science/hal-02918215/file/publi-2020-IJUQ-%28%291-26-arnst-soize-bulthies-preprint.pdf https://doi.org/10.1615/Int.J.UncertaintyQuantification.2020032674 en eng HAL CCSD Begell House Publishers info:eu-repo/semantics/altIdentifier/doi/10.1615/Int.J.UncertaintyQuantification.2020032674 hal-02918215 https://hal.science/hal-02918215 https://hal.science/hal-02918215/document https://hal.science/hal-02918215/file/publi-2020-IJUQ-%28%291-26-arnst-soize-bulthies-preprint.pdf doi:10.1615/Int.J.UncertaintyQuantification.2020032674 info:eu-repo/semantics/OpenAccess ISSN: 2152-5080 EISSN: 2152-5099 International Journal for Uncertainty Quantification https://hal.science/hal-02918215 International Journal for Uncertainty Quantification, 2021, 11 (1), pp.1-23. ⟨10.1615/Int.J.UncertaintyQuantification.2020032674⟩ 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] info:eu-repo/semantics/article Journal articles 2021 ftuniveiffel https://doi.org/10.1615/Int.J.UncertaintyQuantification.2020032674 2024-04-02T17:17:39Z 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. Article in Journal/Newspaper Antarc* Antarctic Ice Sheet HAL Univ-Eiffel (Université Gustave Eiffel) International Journal for Uncertainty Quantification 11 2 1 23 |
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Open Polar |
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HAL Univ-Eiffel (Université Gustave Eiffel) |
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ftuniveiffel |
language |
English |
topic |
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] |
spellingShingle |
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] Arnst, Maarten Soize, Christian Bulthuis, Kevin Computation of Sobol indices in global sensitivity analysis from small data sets by probabilistic learning on manifolds |
topic_facet |
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] |
description |
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. |
author2 |
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 |
author |
Arnst, Maarten Soize, Christian Bulthuis, Kevin |
author_facet |
Arnst, Maarten Soize, Christian Bulthuis, Kevin |
author_sort |
Arnst, Maarten |
title |
Computation of Sobol indices in global sensitivity analysis from small data sets by probabilistic learning on manifolds |
title_short |
Computation of Sobol indices in global sensitivity analysis from small data sets by probabilistic learning on manifolds |
title_full |
Computation of Sobol indices in global sensitivity analysis from small data sets by probabilistic learning on manifolds |
title_fullStr |
Computation of Sobol indices in global sensitivity analysis from small data sets by probabilistic learning on manifolds |
title_full_unstemmed |
Computation of Sobol indices in global sensitivity analysis from small data sets by probabilistic learning on manifolds |
title_sort |
computation of sobol indices in global sensitivity analysis from small data sets by probabilistic learning on manifolds |
publisher |
HAL CCSD |
publishDate |
2021 |
url |
https://hal.science/hal-02918215 https://hal.science/hal-02918215/document https://hal.science/hal-02918215/file/publi-2020-IJUQ-%28%291-26-arnst-soize-bulthies-preprint.pdf https://doi.org/10.1615/Int.J.UncertaintyQuantification.2020032674 |
genre |
Antarc* Antarctic Ice Sheet |
genre_facet |
Antarc* Antarctic Ice Sheet |
op_source |
ISSN: 2152-5080 EISSN: 2152-5099 International Journal for Uncertainty Quantification https://hal.science/hal-02918215 International Journal for Uncertainty Quantification, 2021, 11 (1), pp.1-23. ⟨10.1615/Int.J.UncertaintyQuantification.2020032674⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/doi/10.1615/Int.J.UncertaintyQuantification.2020032674 hal-02918215 https://hal.science/hal-02918215 https://hal.science/hal-02918215/document https://hal.science/hal-02918215/file/publi-2020-IJUQ-%28%291-26-arnst-soize-bulthies-preprint.pdf doi:10.1615/Int.J.UncertaintyQuantification.2020032674 |
op_rights |
info:eu-repo/semantics/OpenAccess |
op_doi |
https://doi.org/10.1615/Int.J.UncertaintyQuantification.2020032674 |
container_title |
International Journal for Uncertainty Quantification |
container_volume |
11 |
container_issue |
2 |
container_start_page |
1 |
op_container_end_page |
23 |
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1797589119327535104 |