Reservoir computing with logistic map
- URL: http://arxiv.org/abs/2401.09501v1
- Date: Wed, 17 Jan 2024 09:22:15 GMT
- Title: Reservoir computing with logistic map
- Authors: R. Arun, M. Sathish Aravindh, A. Venkatesan, M. Lakshmanan
- Abstract summary: We show a method to predict temporal and nontemporal tasks by constructing virtual nodes as constituting a reservoir in reservoir computing.
We predict three nonlinear systems, namely Lorenz, R"ossler, and Hindmarsh-Rose, for temporal tasks and a seventh order for nontemporal tasks.
Remarkably, the logistic map performs well and predicts close to the actual or target values.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Recent studies on reservoir computing essentially involve a high dimensional
dynamical system as the reservoir, which transforms and stores the input as a
higher dimensional state, for temporal and nontemporal data processing. We
demonstrate here a method to predict temporal and nontemporal tasks by
constructing virtual nodes as constituting a reservoir in reservoir computing
using a nonlinear map, namely logistic map, and a simple finite trigonometric
series. We predict three nonlinear systems, namely Lorenz, R\"ossler, and
Hindmarsh-Rose, for temporal tasks and a seventh order polynomial for
nontemporal tasks with great accuracy. Also, the prediction is made in the
presence of noise and found to closely agree with the target. Remarkably, the
logistic map performs well and predicts close to the actual or target values.
The low values of the root mean square error confirm the accuracy of this
method in terms of efficiency. Our approach removes the necessity of continuous
dynamical systems for constructing the reservoir in reservoir computing.
Moreover, the accurate prediction for the three different nonlinear systems
suggests that this method can be considered a general one and can be applied to
predict many systems. Finally, we show that the method also accurately
anticipates the time series for the future (self prediction).
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