基于分布式回声状态网络的混沌系统预测

Distributed Echo State Network for Prediction of Chaotic System

在分析回声状态网络(ESN)的储备池神经元总数和储备池谱半径基础上,提出一种分布式回声状态网络(DESN)的模型.该模型融合了3个大规模的随机稀疏储备池,将其作为信息接收和处理的媒介,将低维的时间序列信息映射到高维空间进行训练,从而提高机器学习效果.在此基础上,通过研究影响每个储备池稳定性的关键参数,确定出神经元总数与谱半径的最佳组合,再通过赋予权重的方式对分布式网络的结构进行优化,从而提高了预测精度和模型的泛化能力,并以典型的Mackey-Glass时滞混沌系统和Lorenz系统为例进行实证分析.通过实验表明,与具有单一储备池的回声状态网络进行直接预测相比,基于分布式回声状态网络的非线性时间序列预测方法提高了动力系统的预测精度,同时增强模型的泛化能力,突显网络性能,克服欠拟合.

The Distributed Echo State Network(DESN)model is proposed to improve the effect of machine learning based on the total number of neurons and the spectral radius of the reservoir in the Echo State Network(ESN).In the novel model DESN,three large-scale random sparse reservoirs are integrated as information receiving and processing media to embed low-dimensional time series in high-dimensional space for training.The optimal combination of the total number of neurons and the spectral radius is determined to improve the stability of each reservoir,and then the structure of the distributed network is optimized by giving weights,thereby improving the prediction accuracy and the generalization ability of the model.To verify the effect of the new model,the typical Mackey-Glass time-delay chaotic system and Lorenz system are taken as examples for empirical analysis.It is shown in the experimental results that the model DESN improves the prediction accuracy of the dynamical system,enhances the generalization ability of the model,and overcomes the under-fitting in the ESN with a single reservoir.