We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor but in its vicinity as well. For this, we consider systems perturbed by an external force. This allows us to not merely predict the time evolution of the system but also study its dynamical properties, such as bifurcations, dynamical response curves, characteristic exponents, etc. It is shown that they can be effectively estimated even in some regions of the state space where no input data were given. We consider several different oscillatory examples, including self-sustained, excitatory, time-delay, and chaotic systems. Furthermore, with a statistical analysis, we assess the amount of training data required for effective inference for two common recurrent neural network cells, the long short-term memory and the gated recurrent unit.
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June 2019
Research Article|
June 26 2019
Inferring the dynamics of oscillatory systems using recurrent neural networks
Rok Cestnik
;
Rok Cestnik
a)
1
Department of Physics and Astronomy, University of Potsdam
, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany
2
Institute for Brain and Behavior Amsterdam and Amsterdam Movement Sciences, Faculty of Behavioural and Movement Sciences, Vrije Universiteit Amsterdam
, van der Boechorststraat 9, 1081BT Amsterdam, The Netherlands
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Markus Abel
Markus Abel
1
Department of Physics and Astronomy, University of Potsdam
, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany
3
Ambrosys GmbH
, David-Gilly-Str. 1, 14469 Potsdam, Germany
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a)
Electronic addresses: [email protected] and [email protected]
Chaos 29, 063128 (2019)
Article history
Received:
March 21 2019
Accepted:
June 06 2019
Citation
Rok Cestnik, Markus Abel; Inferring the dynamics of oscillatory systems using recurrent neural networks. Chaos 1 June 2019; 29 (6): 063128. https://doi.org/10.1063/1.5096918
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