Evolutionary echo state network for long-term time series prediction: on the edge of chaos

Abstract

Quantitative analysis of neural networks is a critical issue to improve their performance. In this paper, we investigate a long-term time series prediction based on the echo state network operating at the edge of chaos. We also assess the eigenfunction of echo state networks and its criticality by the Hermite polynomials. A Hermite polynomial-based activation function design with fast convergence is proposed and the relation between long-term time dependence and edge-of-chaos criticality is given. A new particle swarm optimization-gravitational search algorithm is put forward to improve the parameters estimation that helps attain on the edge of chaos. The method was verified using a chaotic Lorenz system and a real health index data set. The experimental results indicate that evolution makes the reservoir great potential to run on the edge of chaos with rich expression.