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Sobol Tensor Trains for Global Sensitivity Analysis


Ballester-Ripoll, Rafael; Paredes, Enrique G; Pajarola, R (2019). Sobol Tensor Trains for Global Sensitivity Analysis. Reliability Engineering & System Safety, 183:311-322.

Abstract

Sobol indices are a widespread quantitative measure for variance-based global sensitivity analysis, but com- puting and utilizing them remains challenging for high-dimensional systems. We propose the tensor train de- composition (TT) as a unified framework for surrogate modeling and sensitivity analysis via Sobol indices. We first overview several strategies to build a TT surrogate using either an adaptive sampling strategy or a pre- defined set of samples. Our main contribution is the introduction of the Sobol TT, which compactly represents variance components for all possible joint variable interactions of any order. Our formulation allows efficient aggregation and subselection operations, and we are able to obtain related Sobol indices (closed, total, and superset indices) at negligible cost. Furthermore, we exploit an existing global optimization procedure within the TT framework for variable selection and model analysis tasks. We demonstrate our algorithms with two ana- lytical models and a parallel computing simulation data set.

Abstract

Sobol indices are a widespread quantitative measure for variance-based global sensitivity analysis, but com- puting and utilizing them remains challenging for high-dimensional systems. We propose the tensor train de- composition (TT) as a unified framework for surrogate modeling and sensitivity analysis via Sobol indices. We first overview several strategies to build a TT surrogate using either an adaptive sampling strategy or a pre- defined set of samples. Our main contribution is the introduction of the Sobol TT, which compactly represents variance components for all possible joint variable interactions of any order. Our formulation allows efficient aggregation and subselection operations, and we are able to obtain related Sobol indices (closed, total, and superset indices) at negligible cost. Furthermore, we exploit an existing global optimization procedure within the TT framework for variable selection and model analysis tasks. We demonstrate our algorithms with two ana- lytical models and a parallel computing simulation data set.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Informatics
Dewey Decimal Classification:000 Computer science, knowledge & systems
Scopus Subject Areas:Physical Sciences > Safety, Risk, Reliability and Quality
Physical Sciences > Industrial and Manufacturing Engineering
Language:English
Date:March 2019
Deposited On:30 Aug 2019 08:50
Last Modified:21 Jun 2021 07:31
Publisher:Elsevier
ISSN:0951-8320
OA Status:Green
Publisher DOI:https://doi.org/10.1016/j.ress.2018.11.007
Other Identification Number:merlin-id:18071

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