## Abstract

We consider the problem of uncertainty quantification for extreme scale parameter dependent problems where an underlying low rank property of the parameter dependency is assumed. For this type of dependency the hierarchical Tucker format offers a suitable framework to approximate a given output function of the solutions of the parameter dependent problem from a number of samples that is linear in the number of parameters. In particular we can a posteriori compute the mean, variance or other interesting statistical quantities of interest. In the extreme scale setting it is already assumed that the underlying fixed-parameter problem is distributed and solved for in parallel. We provide in addition a parallel evaluation scheme for the sampling phase that allows us on the one hand to combine several solves and on the other hand parallelise the sampling.

Original language | English (US) |
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Pages (from-to) | 67-78 |

Number of pages | 12 |

Journal | Computing and Visualization in Science |

Volume | 17 |

Issue number | 2 |

DOIs | |

State | Published - Aug 23 2015 |

## Keywords

- Hierarchical tucker
- Parallel sampling
- UQ

## ASJC Scopus subject areas

- Theoretical Computer Science
- Software
- Modeling and Simulation
- Engineering(all)
- Computer Vision and Pattern Recognition
- Computational Theory and Mathematics