Abstract
Time-series prediction entails forecasting future values by analysing historical
data to detect patterns, trends, and variations. Two primary approaches
exist: model-based and data-driven methods. Chaotic dynamical systems,
due to their sensitivity on initial conditions, are particularly challenging to
predict. Reservoir computing is a data-driven framework based on recurrent
neural networks. However, unlike traditional machine learning models
that require extensive data and computational power, reservoir computing
leverages an existing dynamical system as a “reservoir”, reducing complexity
while maintaining performance.
This study demonstrates the capability of reservoir computing to both predict
and infer the underlying dynamics of chaotic systems. We trained an RC
model on time-series from the sine, logistic, and H´enon maps. Model performance
was evaluated using standard statistical metrics, including the mean
absolute error, mean square error, and root mean square error, supported by
visual comparisons of actual versus predicted trajectories.
The model achieved reliable short-to-medium-term time-series predictions,
maintaining predictive accuracy for roughly 23–29 time-steps. In addition to
trajectory prediction, our model reconstructed correlation maps that closely
resembled those of the target systems in both shape and structure, estimated
fixed points within two to three decimal places of analytical solutions, and
reproduced Lyapunov exponents accurate to within two decimal places.
These results confirm that reservoir computing serves as a powerful framework
for analysing and forecasting chaotic dynamical systems, demonstrating
that the trained model not only reconstructs the observed trajectories but
also captures the intrinsic structural properties that drive their chaotic behaviour.