Chaotic Time Series Prediction Based On Deep Learning

Chaotic time series is a sequence of time series observed from chaotic systems,because of extreme sensitivity to initial state,its prediction has always been a hot and difficult problem in the field of science.Recently,the development of deep learning technology has promoted its wide application in physics.In particular,the technique known as reservoir computing has attracted more and more attention due to its excellent behavior on chaotic time series prediction,and has formed a new research hotspot.This paper will explore how to effectively predict future time series evolution from the past data of the chaotic systems using deep learning technology,and construct a data-driven model-free framework,which does not depend on prior physical knowledge.In this paper,aiming at the special dynamic characteristics of the chaotic systems,we start from the topological structure of the model and the strategy of assistant predic-tion to construct a model suitable for predicting chaotic time series.In the simulation experiment,we quantify the duration of accurate prediction with the average valid time and use the model to predict the state of Lorenz system.The experiment is divided in-to the topological structure experiment and the strategy experiment.In the topological structure experiment we use RNN、GRU and LSTM as the basic units of the model,construct the training model and predictive model,widely comparing the prediction ef-fect of different topological structures in the chaotic systems,it is proved that LSTM,which can effectively alleviate the gradient problem,is a suitable topological structure for predicting chaotic time series tasks.In the strategy experiment,we use LSTM as the basic model,propose five strategies to assist model prediction,which are suitable for chaotic systems,including normalization and restoration,scaling down the gradients,ESN-based initialization,preserving the best model and resampling training.It Proved that the strategy suitable for chaotic system can greatly improve the prediction effect of the model on chaotic time series.The results show that the prediction ability of the LSTM learning machine with suitable strategies is comparable to that of reservoir computing,furthenrmore,the com-plexity of the LSTM is lower.Therefore,our results indicate that there is no obvious evidence that reservoir computing can surpass the traditional method,which inspires us to further study the mechanism and methods of learning machine for predicting time series,and find more effective learning machines.