Reservoir computing with logistic map

Area of Science:

• Computational neuroscience
• Nonlinear dynamics
• Machine learning

Background:

• Reservoir computing typically uses high-dimensional dynamical systems as reservoirs for data processing.
• Existing methods require complex continuous dynamical systems for reservoir construction.

Purpose of the Study:

• To demonstrate a new method for temporal and nontemporal prediction using virtual nodes in reservoir computing.
• To simplify reservoir construction by avoiding continuous dynamical systems.

Main Methods:

• Constructing virtual nodes using the logistic map (a nonlinear map) and a finite trigonometric series to form the reservoir.
• Predicting nonlinear systems (Lorenz, Rössler, Hindmarsh-Rose) and a seventh-order polynomial.
• Evaluating prediction accuracy in the presence of noise.

Main Results:

• Highly accurate predictions for temporal and nontemporal tasks, including noisy data.
• The logistic map-based reservoir demonstrated excellent performance, closely matching target values.
• Low root mean square error values confirmed the method's efficiency and accuracy.
• Successful self-prediction of the Rössler system's time series variables into the future.

Conclusions:

• The proposed method effectively predicts temporal and nontemporal data using a simplified reservoir construction.
• This approach offers a generalizable and efficient alternative to traditional reservoir computing methods.
• The technique accurately forecasts complex nonlinear systems and noisy data, suggesting wide applicability.