Nearest-neighbor interaction systems in the tensor-train format

Patrick Gelß*, Stefan Klus, Sebastian Matera, Christof Schütte

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)140-162
Number of pages23
JournalJournal of Computational Physics
Publication statusPublished - 15 Jul 2017


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

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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