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Parallel tensor sampling in the hierarchical Tucker format. (English) Zbl 1360.65042
Summary: 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.

MSC:
65C50 Other computational problems in probability (MSC2010)
65Y05 Parallel numerical computation
65C05 Monte Carlo methods
15A69 Multilinear algebra, tensor calculus
68W10 Parallel algorithms in computer science
65Fxx Numerical linear algebra
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