Multidimensional Approximation of Nonlinear Dynamical Systems

Patrick Gelß, Stefan Klus, Jens Eisert, Christof Schütte

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)

Abstract

A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system identification, ranging from industrial engineering and acoustic signal processing to stock market models. In order to find appropriate representations of underlying dynamical systems, various data-driven methods have been proposed by different communities. However, if the given data sets are high-dimensional, then these methods typically suffer from the curse of dimensionality. To significantly reduce the computational costs and storage consumption, we propose the method multidimensional approximation of nonlinear dynamical systems (MANDy) which combines data-driven methods with tensor network decompositions. The efficiency of the introduced approach will be illustrated with the aid of several high-dimensional nonlinear dynamical systems.

Original languageEnglish
Article number061006
JournalJournal of Computational and Nonlinear Dynamics
Volume14
Issue number6
DOIs
Publication statusPublished - Jun 2019

Keywords

  • data-driven methods
  • nonlinear dynamics
  • system identification
  • tensor networks
  • tensor-train format

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Mechanical Engineering
  • Applied Mathematics

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