Repository: Freie Universit├Ąt Berlin, Math Department

Approximating turbulent and non-turbulent events with the Tensor Train decomposition method

von Larcher, T. and Klein, R. (2019) Approximating turbulent and non-turbulent events with the Tensor Train decomposition method. In: Turbulent Cascades II. Springer. ISBN Print: 978-3-030-12546-2 Electronic: 978-3-030-12547-9

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Official URL: https://doi.org/10.1007/978-3-030-12547-9_30

Abstract

Low-rank multilevel approximation methods are often suited to attack high-dimensional problems successfully and they allow very compact representation of large data sets. Specifically, hierarchical tensor product decomposition methods, e.g., the Tree-Tucker format and the Tensor Train format emerge as a promising approach for application to data that are concerned with cascade-of-scales 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 self-similar 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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