The polynomial dimensional decomposition (PDD) is employed in this work for theglobal sensitivity analysis and uncertainty quantification (UQ) of stochastic systems subject to amoderate to large number of input random variables. Due to the intimate structure between thePDD and the Analysis of Variance (ANOVA) approach, PDD is able to provide a simpler and moredirect evaluation of the Sobol’ sensitivity indices, when compared to the Polynomial Chaos expansion(PC). Unfortunately, the number of PDD terms grows exponentially with respect to the sizeof the input random vector, which makes the computational cost of standard methods unaffordablefor real engineering applications. In order to address the problem of the curse of dimensionality, thiswork proposes essentially variance-based adaptive strategies aiming to build a cheap meta-model(i.e. surrogate model) by employing the sparse PDD approach with its coefficients computed byregression. Three levels of adaptivity are carried out in this paper: 1) the truncated dimensionalityfor ANOVA component functions, 2) the active dimension technique especially for second- andhigher-order parameter interactions, and 3) the stepwise regression approach designed to retainonly the most influential polynomials in the PDD expansion. During this adaptive procedure featuringstepwise regressions, the surrogate model representation keeps containing few terms, so thatthe cost to resolve repeatedly the linear systems of the least-square regression problem is negligible.The size of the finally obtained sparse PDD representation is much smaller than the one of the fullexpansion, since only significant terms are eventually retained. Consequently, a much less numberof calls to the deterministic model is required to compute the final PDD coefficients.Read less <