Keynote lecture by Bruno Sudret

Surrogate models for global sensitivity analysis – Old and New

Abstract

Sensitivity analysis of model outputs (SAMO) aims at determining what are the important random input parameters that influence the most the response of a computer code. Variance-based sensitivity analysis and related Sobol’ indices allow the analyst to decompose the variance of the model output into contributions of each input parameter taken separately, and joint contributions of pairs, triplets, etc. of parameters. Other methods include distribution-based sensitivity indices and dependence measures.

The standard approach to estimate these indices often relies on Monte Carlo simulation, which leads to huge computational costs (typically O (104−6) runs of the computer code). This is practically intractable for realistic computational models, unless they are replaced by properly calibrated surrogate models.

In this talk we will review how different types of surrogate models such as (sparse) polynomial chaos expansions, low-rank tensor approximations and Kriging can be suitably used to estimate Sobol’- and distribution-based sensitivity indices (Le Gratiet et al., 2016; Konakli and Sudret, 2016). Recent developments in the context of the modelling of epistemic uncertainty through imprecise probability theory will eventually be reported (Schöbi and Sudret, 2017).

References

Konakli, K. and B. Sudret (2016). Global sensitivity analysis using low-rank tensor approximations. Reliab. Eng. Sys. Safety 156, 64–83.

Le Gratiet, L., S. Marelli, and B. Sudret (2016). Metamodel-based sensitivity analysis: polynomial chaos expansions and Gaussian processes, in Handbook on Uncertainty Quantification, R. Ghanem, D. Higdon and H. Owhadi (Eds.), Chapter 8. Springer.

Schöbi, R. and B. Sudret (2017). PCE-based imprecise Sobol’ indices. In C. Bucher (Ed.), Proc. 12th Int. Conf. Struct. Safety and Reliability (ICOSSAR’2017), Vienna, Austria.

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