Adaptive surrogate modeling by ANOVA and sparse polynomial dimensional decomposition for global sensitivity analysis in fluids simulation
Abstract
The polynomial dimensional decomposition (PDD) is employed in this work for the
global sensitivity analysis and uncertainty quantification (UQ) of stochastic systems subject to a
moderate to large number of input random variables. Due to the intimate structure between the
PDD and the Analysis of Variance (ANOVA) approach, PDD is able to provide a simpler and more
direct 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 size
of the input random vector, which makes the computational cost of standard methods unaffordable
for real engineering applications. In order to address the problem of the curse of dimensionality, this
work 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 by
regression. Three levels of adaptivity are carried out in this paper: 1) the truncated dimensionality
for ANOVA component functions, 2) the active dimension technique especially for second- and
higher-order parameter interactions, and 3) the stepwise regression approach designed to retain
only the most influential polynomials in the PDD expansion. During this adaptive procedure featuring
stepwise regressions, the surrogate model representation keeps containing few terms, so that
the 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 full
expansion, since only significant terms are eventually retained. Consequently, a much less number
of calls to the deterministic model is required to compute the final PDD coefficients.
Origin : Files produced by the author(s)
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