Repository: Freie Universität Berlin, Math Department

Nearest-neighbor interaction systems in the tensor-train format

Gelß, P. and Klus, S. and Matera, S. and Schütte, Ch. (2017) Nearest-neighbor interaction systems in the tensor-train format. Journal of Computational Physics, 341 . pp. 140-162. ISSN 0021-9991



Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods anymore due to the so-called curse of dimensionality. This requires techniques to handle linear operators defined on extremely large state spaces and to solve the resulting systems of linear equations or eigenvalue problems. In this paper, we present a systematic tensor-train decomposition for nearest-neighbor interaction systems which is applicable to a host of different problems. With the aid of this decomposition, it is possible to reduce the memory consumption as well as the computational costs significantly. Furthermore, it can be shown that in some cases the rank of the tensor decomposition does not depend on the network size. The format is thus feasible even for high-dimensional systems. We will illustrate the results with several guiding examples such as the Ising model, a system of coupled oscillators, and a CO oxidation model.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group
ID Code:2097
Deposited By: Ulrike Eickers
Deposited On:22 Aug 2017 11:03
Last Modified:28 Sep 2017 15:22

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