  In the context of global sensitivity analysis, the Sobol' indices constitute
a powerful tool for assessing the relative significance of the uncertain input
parameters of a model. We herein introduce a novel approach for evaluating
these indices at low computational cost, by post-processing the coefficients of
polynomial meta-models belonging to the class of low-rank tensor
approximations. Meta-models of this class can be particularly efficient in
representing responses of high-dimensional models, because the number of
unknowns in their general functional form grows only linearly with the input
dimension. The proposed approach is validated in example applications, where
the Sobol' indices derived from the meta-model coefficients are compared to
reference indices, the latter obtained by exact analytical solutions or
Monte-Carlo simulation with extremely large samples. Moreover, low-rank tensor
approximations are confronted to the popular polynomial chaos expansion
meta-models in case studies that involve analytical rank-one functions and
finite-element models pertinent to structural mechanics and heat conduction. In
the examined applications, indices based on the novel approach tend to converge
faster to the reference solution with increasing size of the experimental
design used to build the meta-model.
