A Hybrid Method Using HAVOK Analysis and Machine Learning for Predicting Chaotic Time Series.

Jinhui Yang,Chengwu Zhao,Hongze Leng,Jianping Wu,Juan Zhao,Junqiang Song

doi:10.3390/e24030408

Abstract

The prediction of chaotic time series systems has remained a challenging problem in recent decades. A hybrid method using Hankel Alternative View Of Koopman (HAVOK) analysis and machine learning (HAVOK-ML) is developed to predict chaotic time series. HAVOK-ML simulates the time series by reconstructing a closed linear model so as to achieve the purpose of prediction. It decomposes chaotic dynamics into intermittently forced linear systems by HAVOK analysis and estimates the external intermittently forcing term using machine learning. The prediction performance evaluations confirm that the proposed method has superior forecasting skills compared with existing prediction methods.

Highlights

A chaotic system refers to a deterministic system where there are irregular movements that appear to be random, and its behavior is uncertain, unrepeatable, and unpredictable
It can be shown that the Root Mean Squared Error (RMSE) index of the proposed method is optimal, while the NMSE index shows that the proposed method is second only to the functional weight wavelet neural network (WNN) state-dependent AR (FWWNN-AR) model [15]
Based on the Hankel Alternative View Of Koopman (HAVOK) analysis, the observed chaotic dynamic system could be reconstructed as a linear model with an external intermittent forcing

Summary

Introduction

A chaotic system refers to a deterministic system where there are irregular movements that appear to be random, and its behavior is uncertain, unrepeatable, and unpredictable. To simplify the learning model, a hybrid method using Hankel Alternative View Of Koopman (HAVOK) analysis and machine learning (HAVOK-ML) is developed to predict chaotic time series in this research. Hankel Alternative View Of Koopman (HAVOK) analysis was proposed by Brunton [22] It combines the delay embedding method [23] and the Koopman theory [24] to decompose chaotic dynamics into a linear model with intermittent forcing. The prediction of the chaotic time series using the HAVOK-ML method is conducted as solving linear ordinary differential equations, which can be calculated efficiently It can take different types of regression methods such as Linear Regression or Random Forest Regression (RFR) [25] into the prediction framework and combines the advantages of HAVOK theory and machine learning. The R2 score is used to evaluate the score of the machine learning based prediction for vr

Lorenz Time Series

Mackey–Glass Time Series

Sunspot Time Series

Discussion and Conclusions