Inferring the dynamics of oscillatory systems using recurrent neural networks

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 dyna...

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Bibliographic Details
Published in:arXiv.org 2019-06
Main Authors: Rok Cestnik, Abel, Markus
Format: Article
Language:English
Subjects:
Bifurcations
Chaos theory
Neural networks
Recurrent neural networks
Statistical analysis
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1904.03026