scholarly journals Data-driven Evolution Equation Reconstruction for Parameter-Dependent Nonlinear Dynamical Systems

2018 ◽  
Vol 58 (6-7) ◽  
pp. 787-794 ◽  
Author(s):  
David W. Sroczynski ◽  
Or Yair ◽  
Ronen Talmon ◽  
Ioannis G. Kevrekidis
Keyword(s):  
Dynamical Systems ◽  
Evolution Equation ◽  
Nonlinear Dynamical Systems ◽  
Data Driven ◽  
Nonlinear Dynamical ◽  
Parameter Dependent

scholarly journals Multidimensional Approximation of Nonlinear Dynamical Systems

2019 ◽  
Vol 14 (6) ◽  
Author(s):  
Patrick Gelß ◽  
Stefan Klus ◽  
Jens Eisert ◽  
Christof Schütte
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Measurement Data ◽  
Data Driven ◽  
High Dimensional ◽  
Data Sets ◽  
Nonlinear Dynamical ◽  
Tensor Network ◽  
Wide Range ◽  
Multidimensional Approximation

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.

A data-driven approach to model calibration for nonlinear dynamical systems

2019 ◽  
Vol 125 (24) ◽  
pp. 244901 ◽  
Author(s):  
C. M. Greve ◽  
K. Hara ◽  
R. S. Martin ◽  
D. Q. Eckhardt ◽  
J. W. Koo
Keyword(s):  
Dynamical Systems ◽  
Model Calibration ◽  
Nonlinear Dynamical Systems ◽  
Data Driven ◽  
Nonlinear Dynamical ◽  
Data Driven Approach
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