Efficient Solution of Ordinary Differential Equations with High-Dimensional Parametrized Uncertainty

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 hundred of parameters. We demonstrate the accuracy and efficiency of this approach on a number of challenging test cases drawn from engineering and science.


Published in:
Communications in Computational Physics, 10, 2, 253-278
Year:
2011
Publisher:
GLOBAL SCIENCE PRESS
ISSN:
1815-2406
Keywords:
Laboratories:




 Record created 2013-11-12, last modified 2018-01-28

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