@Article{CiCP-10-2,
author = {},
title = {Efficient Solution of Ordinary Differential Equations with High-Dimensional Parametrized Uncertainty},
journal = {Communications in Computational Physics},
year = {2011},
volume = {10},
number = {2},
pages = {253--278},
abstract = {<p style="text-align: justify;">The important task of evaluating the impact of random parameters on the
output of stochastic ordinary differential equations (SODE) can be computationally
very demanding, in particular for problems with a high-dimensional parameter space.
In this work we consider this problem in some detail and demonstrate that by combining
several techniques one can dramatically reduce the overall cost without impacting
the predictive accuracy of the output of interests. We discuss how the combination of
ANOVA expansions, different sparse grid techniques, and the total sensitivity index
(TSI) as a pre-selective mechanism enables the modeling of problems with hundreds of
parameters. We demonstrate the accuracy and efficiency of this approach on a number
of challenging test cases drawn from engineering and science.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.090110.080910a},
url = {https://global-sci.com/article/80922/efficient-solution-of-ordinary-differential-equations-with-high-dimensional-parametrized-uncertainty}
}