Header

UZH-Logo

Maintenance Infos

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 computing and utilizing them remains challenging for high-dimensional systems. We propose the tensor train decomposition (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 predefined 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 analytical models and a parallel computing simulation data set.

Abstract

Sobol indices are a widespread quantitative measure for variance-based global sensitivity analysis, but computing and utilizing them remains challenging for high-dimensional systems. We propose the tensor train decomposition (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 predefined 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 analytical models and a parallel computing simulation data set.

Statistics

Citations

Dimensions.ai Metrics
13 citations in Web of Science®
13 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

62 downloads since deposited on 30 Aug 2019
38 downloads since 12 months
Detailed statistics

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:26 Jan 2022 22:22
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

Download

Green Open Access

Download PDF  'Sobol Tensor Trains for Global Sensitivity Analysis'.
Preview
Content: Accepted Version
Filetype: PDF
Size: 3MB
View at publisher
Licence: Creative Commons: Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)