WOA-Based Echo State Network for Chaotic Time Series Prediction

We present a new chaotic times prediction model inspired by the bubble-net predation of whales. The echo state network (ESN) is a new type of recurrent neural network. However, selecting parameters empirically for the ESN cannot guarantee the accuracy of the prediction. The whale optimization algorithm (WOA) imitates the bubble-net predation of whales and ensures the rapid convergence of selecting network parameters. A new prediction model, WOA-ESN, in which the WOA and the ESN are incorporated, is proposed in this paper. In addition, a simplified cross-validation (CV) method is proposed to take into account the approximation performance and generalization ability of the WOA-ESN. In experiments, the WOA-ESN is used for Mackey-Glass and Lorenz chaotic time series predictions, and the results are compared with the ESN based on particle swarm optimization (PSO-ESN), the ESN based on genetic algorithm (GA-ESN), and ESN. The results show that the proposed model has the best prediction performance.