Volume 10, Issue 2
Efficient Solution of Ordinary Differential Equations with High-Dimensional Parametrized Uncertainty

Zhen Gao & Jan S. Hesthaven

Commun. Comput. Phys., 10 (2011), pp. 253-278.

Published online: 2011-10

Preview Full PDF 131 1035
Export citation
  • 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 hundred of parameters. We demonstrate the accuracy and efficiency of this approach on a number of challenging test cases drawn from engineering and science.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-10-253, 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 = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.090110.080910a}, url = {http://global-sci.org/intro/article_detail/cicp/7442.html} }
TY - JOUR T1 - Efficient Solution of Ordinary Differential Equations with High-Dimensional Parametrized Uncertainty JO - Communications in Computational Physics VL - 2 SP - 253 EP - 278 PY - 2011 DA - 2011/10 SN - 10 DO - http://dor.org/10.4208/cicp.090110.080910a UR - https://global-sci.org/intro/article_detail/cicp/7442.html KW - AB -

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.

Zhen Gao & Jan S. Hesthaven. (2020). Efficient Solution of Ordinary Differential Equations with High-Dimensional Parametrized Uncertainty. Communications in Computational Physics. 10 (2). 253-278. doi:10.4208/cicp.090110.080910a
Copy to clipboard
The citation has been copied to your clipboard