von Larcher, T. and Klein, R. (2019) Approximating turbulent and nonturbulent events with the Tensor Train decomposition method. In: Turbulent Cascades II. Springer. ISBN Print: 9783030125462 Electronic: 9783030125479

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Official URL: https://doi.org/10.1007/9783030125479_30
Abstract
Lowrank multilevel approximation methods are often suited to attack highdimensional problems successfully and they allow very compact representation of large data sets. Specifically, hierarchical tensor product decomposition methods, e.g., the TreeTucker format and the Tensor Train format emerge as a promising approach for application to data that are concerned with cascadeofscales problems as, e.g., in turbulent fluid dynamics. Beyond multilinear mathematics, those tensor formats are also successfully applied in e.g., physics or chemistry, where they are used in many body problems and quantum states. Here, we focus on two particular objectives, that is, we aim at capturing selfsimilar structures that might be hidden in the data and we present the reconstruction capabilities of the Tensor Train decomposition method tested with 3D channel turbulence flow data.
Item Type:  Book Section 

Additional Information:  SFB 1114 Preprint: 11/2017 
Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group 
ID Code:  2199 
Deposited By:  Silvia Hoemke 
Deposited On:  09 Feb 2018 14:45 
Last Modified:  26 Aug 2019 15:01 
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