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Sobol tensor trains for global sensitivity analysis

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  • Ballester-Ripoll, Rafael
  • Paredes, Enrique G.
  • Pajarola, Renato

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.

Suggested Citation

  • Ballester-Ripoll, Rafael & Paredes, Enrique G. & Pajarola, Renato, 2019. "Sobol tensor trains for global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 311-322.
    • Handle: RePEc:eee:reensy:v:183:y:2019:i:c:p:311-322
    DOI: 10.1016/j.ress.2018.11.007
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    1. Marrel, Amandine & Iooss, Bertrand & Laurent, Béatrice & Roustant, Olivier, 2009. "Calculations of Sobol indices for the Gaussian process metamodel," Reliability Engineering and System Safety, Elsevier, vol. 94(3), pages 742-751.
    2. Ledyard Tucker, 1966. "Some mathematical notes on three-mode factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 279-311, September.
    3. Wu, Zeping & Wang, Donghui & Okolo N, Patrick & Hu, Fan & Zhang, Weihua, 2016. "Global sensitivity analysis using a Gaussian Radial Basis Function metamodel," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 171-179.
    4. Sudret, Bruno, 2008. "Global sensitivity analysis using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 964-979.
    5. Konakli, Katerina & Sudret, Bruno, 2016. "Global sensitivity analysis using low-rank tensor approximations," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 64-83.
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    1. Ballester-Ripoll, Rafael & Leonelli, Manuele, 2022. "Computing Sobol indices in probabilistic graphical models," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    2. Vuillod, Bruno & Montemurro, Marco & Panettieri, Enrico & Hallo, Ludovic, 2023. "A comparison between Sobol’s indices and Shapley’s effect for global sensitivity analysis of systems with independent input variables," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    3. Serafino, Aldo & Obert, Benoit & Vergé, Léa & Cinnella, Paola, 2020. "Robust optimization of an organic Rankine cycle for geothermal application," Renewable Energy, Elsevier, vol. 161(C), pages 1120-1129.

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