期刊
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS
卷 14, 期 6, 页码 -出版社
ASME
DOI: 10.1115/1.4043148
关键词
nonlinear dynamics; system identification; data-driven methods; tensor networks; tensor-train format
资金
- Deutsche Forschungsgemeinschaft [CRC 1114, EI 519/9-1]
- European Research Council (TAQ)
- John Templeton Foundation [58188]
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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