R. Arun, M. Sathish Aravindh, A. Venkatesan, M. Lakshmanan
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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, the logistic map, and a simple finite trigonometric series. We predict three nonlinear systems, namely, Lorenz, Rössler, 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 of the all the three variable of Rössler system for the future (self-prediction).
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.