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research-article

Multidimensional approximation of nonlinear dynamical systems

[+] Author and Article Information
Patrick Gelß

Department of Mathematics and Computer Science, Freie Universität Berlin, Germany
p.gelss@fu-berlin.de

Stefan Klus

Department of Mathematics and Computer Science, Freie Universität Berlin, Germany
stefan.klus@fu-berlin.de

Jens Eisert

Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Germany
jense@zedat.fu-berlin.de

Christof Schütte

Department of Mathematics and Computer Science, Freie Universität Berlin, Germany; Zuse Institute Berlin, Germany
christof.schuette@fu-berlin.de

1Corresponding author.

ASME doi:10.1115/1.4043148 History: Received October 09, 2018; Revised March 05, 2019

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 in 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 will therefore combine 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.

Copyright (c) 2019 by ASME
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