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Hierarchical Low Rank Tensors

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UNQW03 - Reducing dimensions and cost for UQ in complex systems

Co-authors: Sebastian Krämer, Christian Löbbert, Dieter Moser (RWTH Aachen) We introduce the concept of hierarchical low rank decompositions and approximations by use of the hierarchical Tucker format. In order to relate it to several other existing low rank formats we highlight differences, similarities as well as bottlenecks of these. One particularly difficult question is whether or not a tensor or multivariate function allows a priori a low rank representation or approximation. This question can be related to simple matrix decompositions or approximations, but still the question is not easy to answer, cf. the talks of Wolfgang Dahmen, Sergey Dolgov, Martin Stoll and Anthony Nouy. We provide numerical evidence for a model problem that the approximation can be efficient in terms of a small rank. In order to find such a decomposition or approximation we consider black box (cross) type non-intrusive sampling approaches. A special emphasis will be on postprocessing of the tensors, e.g. finding extremal points efficiently. This is of special interest in the context of model reduction and reliability analysis.

This talk is part of the Isaac Newton Institute Seminar Series series.

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