Tensor-based computation of metastable and coherent sets

Feliks Nüske*, Patrick Gelß, Stefan Klus, Cecilia Clementi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations – in particular the tensor train (TT) format – have become a valuable tool for the solution of large-scale problems in a number of fields. In this work, we combine Koopman-based models and the TT format, enabling their application to high-dimensional problems in conjunction with a rich set of basis functions or features. We derive efficient algorithms to obtain a reduced matrix representation of the system's evolution operator starting from an appropriate low-rank representation of the data. These algorithms can be applied to both stationary and non-stationary systems. We establish the infinite-data limit of these matrix representations, and demonstrate our methods’ capabilities using several benchmark data sets.

Original languageEnglish
Article number133018
JournalPhysica D: Nonlinear Phenomena
Early online date6 Sept 2021
Publication statusPublished - Dec 2021


  • Dynamical systems
  • Extended dynamic mode decomposition
  • Koopman operator
  • Molecular dynamics
  • Tensor networks
  • Tensor-train format

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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