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

Efficient Solution of Ordinary Differential Equations with High-Dimensional Parametrized Uncertainty
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Year:    2011

Communications in Computational Physics, Vol. 10 (2011), Iss. 2 : pp. 253–278

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.090110.080910a

Communications in Computational Physics, Vol. 10 (2011), Iss. 2 : pp. 253–278

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords:   

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