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Parallel tensor sampling in the hierarchical Tucker format

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Computing and Visualization in Science

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.

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Notes

  1. The root is not relevant and for the two sons of it the matricizations are the transposed of each other

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Authors and Affiliations

  1. IGPM, RWTH-Aachen, Templergraben 55, 52056, Aachen, Germany

    Lars Grasedyck & Christian Löbbert

  2. MPI MIS Leipzig, Inselstraße 22, 04103, Leipzig, Germany

    Ronald Kriemann

  3. G-CSC, Univ. Frankfurt, Kettenhofweg 139, 60325, Frankfurt am Main, Germany

    Arne Nägel, Gabriel Wittum & Konstantinos Xylouris

Authors
  1. Lars Grasedyck
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  2. Ronald Kriemann
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  3. Christian Löbbert
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  4. Arne Nägel
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  5. Gabriel Wittum
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  6. Konstantinos Xylouris
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Corresponding author

Correspondence to Lars Grasedyck.

Additional information

Communicated by Volker Schulz.

The first three authors gratefully acknowledge support from the DFG priority programme 1648 (SPPEXA) under Grant No. GR-3179/4-1, the last three authors under Grant No. WI-1037/24-1.

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Grasedyck, L., Kriemann, R., Löbbert, C. et al. Parallel tensor sampling in the hierarchical Tucker format. Comput. Visual Sci. 17, 67–78 (2015). https://doi.org/10.1007/s00791-015-0247-x

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  • DOI: https://doi.org/10.1007/s00791-015-0247-x

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