160 research outputs found
Computing derivative-based global sensitivity measures using polynomial chaos expansions
In the field of computer experiments sensitivity analysis aims at quantifying
the relative importance of each input parameter (or combinations thereof) of a
computational model with respect to the model output uncertainty. Variance
decomposition methods leading to the well-known Sobol' indices are recognized
as accurate techniques, at a rather high computational cost though. The use of
polynomial chaos expansions (PCE) to compute Sobol' indices has allowed to
alleviate the computational burden though. However, when dealing with large
dimensional input vectors, it is good practice to first use screening methods
in order to discard unimportant variables. The {\em derivative-based global
sensitivity measures} (DGSM) have been developed recently in this respect. In
this paper we show how polynomial chaos expansions may be used to compute
analytically DGSMs as a mere post-processing. This requires the analytical
derivation of derivatives of the orthonormal polynomials which enter PC
expansions. The efficiency of the approach is illustrated on two well-known
benchmark problems in sensitivity analysis
Derivative-based global sensitivity measures: general links with Sobol' indices and numerical tests
The estimation of variance-based importance measures (called Sobol' indices)
of the input variables of a numerical model can require a large number of model
evaluations. It turns to be unacceptable for high-dimensional model involving a
large number of input variables (typically more than ten). Recently, Sobol and
Kucherenko have proposed the Derivative-based Global Sensitivity Measures
(DGSM), defined as the integral of the squared derivatives of the model output,
showing that it can help to solve the problem of dimensionality in some cases.
We provide a general inequality link between DGSM and total Sobol' indices for
input variables belonging to the class of Boltzmann probability measures, thus
extending the previous results of Sobol and Kucherenko for uniform and normal
measures. The special case of log-concave measures is also described. This link
provides a DGSM-based maximal bound for the total Sobol indices. Numerical
tests show the performance of the bound and its usefulness in practice
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