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.

中文翻译：

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进化回波状态网络用于长期时间序列预测：处于混沌边缘

摘要

对神经网络进行定量分析是提高其性能的关键问题。在本文中，我们研究了基于混沌边缘运行的回波状态网络的长期时间序列预测。我们还通过Hermite多项式评估回波状态网络的本征函数及其临界性。提出了一种基于Hermite多项式的快速收敛激活函数设计方法，并给出了长期时间依赖性和混沌边缘临界度之间的关系。提出了一种新的粒子群优化-引力搜索算法，以改进参数估计，有助于达到混沌的边缘。该方法已使用混沌Lorenz系统和真实健康指数数据集进行了验证。