Echo State Networks for the Prediction of Chaotic Systems

Chaotic systems are complex and challenging to predict due to their sensitive dependence on initial conditions and the complexity of their dynamics. This paper improves the prediction accuracy of chaotic systems using Echo State Networks (ESNs) by considering a complex graph adjacency matrix as the recurrent layer. This helps ESNs better capture the nonlinear dynamics of chaotic systems. ESNs are a type of recurrent neural network with a fixed, randomly generated hidden layer, making them computationally efficient and able to handle large, high-dimensional datasets. This study applies ESNs to the Lorenz, Mackey-Glass, and Kuramoto-Sivashinsky models, which are well-studied examples of chaotic systems. Our results demonstrate that ESNs can effectively capture the dynamics of these systems and outperform existing prediction methods made with ESNs.