Sobol tensor trains for global sensitivity analysis
| Autor: | Rafael Ballester-Ripoll, E. G. Paredes, Renato Pajarola |
|---|---|
| Přispěvatelé: | University of Zurich, Ballester-Ripoll, Rafael |
| Rok vydání: | 2019 |
| Předmět: |
021110 strategic
defence & security studies 021103 operations research Adaptive sampling 10009 Department of Informatics Computer science Computer Science - Numerical Analysis 0211 other engineering and technologies Sobol sequence Feature selection Low-rank approximation Numerical Analysis (math.NA) 02 engineering and technology Variance (accounting) Subset and superset 000 Computer science knowledge & systems Industrial and Manufacturing Engineering 2213 Safety Risk Reliability and Quality FOS: Mathematics 65C20 15A69 49Q12 Sensitivity (control systems) 2209 Industrial and Manufacturing Engineering Safety Risk Reliability and Quality Global optimization Algorithm |
| Zdroj: | Reliability Engineering & System Safety. 183:311-322 |
| ISSN: | 0951-8320 |
| DOI: | 10.1016/j.ress.2018.11.007 |
| Popis: | 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 global sensitivity analysis via Sobol indices. We first overview several strategies to build a TT surrogate of the unknown true model using either an adaptive sampling strategy or a predefined set of samples. We then introduce and derive the Sobol tensor train, which compactly represents the Sobol indices for all possible joint variable interactions which are infeasible to compute and store explicitly. Our formulation allows efficient aggregation and subselection operations: we are able to obtain related 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 engineering models and a parallel computing simulation data set. |
| Databáze: | OpenAIRE |
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