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.
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June 2019
Research-Article
Multidimensional Approximation of Nonlinear Dynamical Systems
Patrick Gelß,
Patrick Gelß
Department of Mathematics and
Computer Science,
Freie Universität,
Berlin 14195, Germany
Computer Science,
Freie Universität,
Berlin 14195, Germany
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Stefan Klus,
Stefan Klus
Department of Mathematics and
Computer Science,
Freie Universität,
Berlin 14195, Germany
Computer Science,
Freie Universität,
Berlin 14195, Germany
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Jens Eisert,
Jens Eisert
Dahlem Center for Complex Quantum Systems,
Freie Universität,
Berlin 14195, Germany
Freie Universität,
Berlin 14195, Germany
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Christof Schütte
Christof Schütte
Department of Mathematics and
Computer Science,
Freie Universität,
Berlin 14195, Germany;
Computer Science,
Freie Universität,
Berlin 14195, Germany;
Zuse Institute,
Berlin 14195, Germany
Berlin 14195, Germany
Search for other works by this author on:
Patrick Gelß
Department of Mathematics and
Computer Science,
Freie Universität,
Berlin 14195, Germany
Computer Science,
Freie Universität,
Berlin 14195, Germany
Stefan Klus
Department of Mathematics and
Computer Science,
Freie Universität,
Berlin 14195, Germany
Computer Science,
Freie Universität,
Berlin 14195, Germany
Jens Eisert
Dahlem Center for Complex Quantum Systems,
Freie Universität,
Berlin 14195, Germany
Freie Universität,
Berlin 14195, Germany
Christof Schütte
Department of Mathematics and
Computer Science,
Freie Universität,
Berlin 14195, Germany;
Computer Science,
Freie Universität,
Berlin 14195, Germany;
Zuse Institute,
Berlin 14195, Germany
Berlin 14195, Germany
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 9, 2018; final manuscript received March 5, 2019; published online April 8, 2019. Assoc. Editor: Katrin Ellermann.
J. Comput. Nonlinear Dynam. Jun 2019, 14(6): 061006 (12 pages)
Published Online: April 8, 2019
Article history
Received:
October 9, 2018
Revised:
March 5, 2019
Citation
Gelß, P., Klus, S., Eisert, J., and Schütte, C. (April 8, 2019). "Multidimensional Approximation of Nonlinear Dynamical Systems." ASME. J. Comput. Nonlinear Dynam. June 2019; 14(6): 061006. https://doi.org/10.1115/1.4043148
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