Nearest-neighbor interaction systems in the tensor-train format

JOURNAL OF COMPUTATIONAL PHYSICS

卷:341

Article

Gelss, Patrick¹  Klus, Stefan¹  Matera, Sebastian¹  Schuette, Christof^1,2 

[1] Free Univ Berlin, Dept Math & Comp Sci, Berlin, Germany

[2] Zuse Inst Berlin, Berlin, Germany

关键词: Tensor decompositions;    Tensor-train format;    Nearest-neighbor interactions;    Ising models;    Linearly coupled oscillators;    Markovian master equation;    Heterogeneous catalysis;    Queuing problems;   

DOI  :  10.1016/j.jcp.2017.04.007

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free