Adaptive Hierarchical Low Rank Formats of High-dimensional Tensors with Applications in PDEs with Stochastic Parameters

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The aim of this research proposal is the further development of the data-sparse hierarchical tensor representations (hierarchical Tucker and TT) from the first phase of this project. Our goal is to introduce a dimension-adaptivity as well as a local separation technique. The latter one is required for the application to partial differential equations with stochastic parameters, as the deterministic space dependent variables are typically strongly linked to local parameters and thus destroy the (global) separability of deterministic and stochastic variables. Both techniques are not restricted to the aforementioned application area as they are of general interest for the understanding of hierarchical tensor formats.