Gelß, P. and Klus, S. and Matera, S. and Schütte, Ch. (2017) Nearestneighbor interaction systems in the tensortrain format. Journal of Computational Physics, 341 . pp. 140162. ISSN 00219991

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Abstract
Lowrank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of highdimensional problems which cannot be solved using conventional methods anymore due to the socalled 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 tensortrain decomposition for nearestneighbor 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 highdimensional 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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