Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Predicting Chaotic System Behavior using Machine Learning Techniques

Huaiyuan Rao, Yichen Zhao, Qiang Lai

TL;DR

This work evaluates three machine learning approaches for forecasting chaotic dynamics: LSTM, RC, and NG-RC, across four canonical chaotic systems. NG-RC emerges as the most computationally efficient and data-efficient method, capable of long-horizon predictions with interpretable linear and nonlinear feature contributions, and demonstrates robustness to noise comparable to RC. LSTM struggles with long-horizon chaotic forecasting, highlighting limitations of recursive error propagation in such settings. The findings suggest NG-RC as a promising tool for real-time chaotic system prediction and digital-twin applications, especially when data are scarce or noisy. The study broadens understanding of data-driven chaotic forecasting and points to practical, interpretable modeling with NG-RC in engineering contexts.

Abstract

Recently, machine learning techniques, particularly deep learning, have demonstrated superior performance over traditional time series forecasting methods across various applications, including both single-variable and multi-variable predictions. This study aims to investigate the capability of i) Next Generation Reservoir Computing (NG-RC) ii) Reservoir Computing (RC) iii) Long short-term Memory (LSTM) for predicting chaotic system behavior, and to compare their performance in terms of accuracy, efficiency, and robustness. These methods are applied to predict time series obtained from four representative chaotic systems including Lorenz, Rössler, Chen, Qi systems. In conclusion, we found that NG-RC is more computationally efficient and offers greater potential for predicting chaotic system behavior.

Predicting Chaotic System Behavior using Machine Learning Techniques

TL;DR

This work evaluates three machine learning approaches for forecasting chaotic dynamics: LSTM, RC, and NG-RC, across four canonical chaotic systems. NG-RC emerges as the most computationally efficient and data-efficient method, capable of long-horizon predictions with interpretable linear and nonlinear feature contributions, and demonstrates robustness to noise comparable to RC. LSTM struggles with long-horizon chaotic forecasting, highlighting limitations of recursive error propagation in such settings. The findings suggest NG-RC as a promising tool for real-time chaotic system prediction and digital-twin applications, especially when data are scarce or noisy. The study broadens understanding of data-driven chaotic forecasting and points to practical, interpretable modeling with NG-RC in engineering contexts.

Abstract

Recently, machine learning techniques, particularly deep learning, have demonstrated superior performance over traditional time series forecasting methods across various applications, including both single-variable and multi-variable predictions. This study aims to investigate the capability of i) Next Generation Reservoir Computing (NG-RC) ii) Reservoir Computing (RC) iii) Long short-term Memory (LSTM) for predicting chaotic system behavior, and to compare their performance in terms of accuracy, efficiency, and robustness. These methods are applied to predict time series obtained from four representative chaotic systems including Lorenz, Rössler, Chen, Qi systems. In conclusion, we found that NG-RC is more computationally efficient and offers greater potential for predicting chaotic system behavior.
Paper Structure (14 sections, 12 equations, 15 figures, 2 tables)

This paper contains 14 sections, 12 equations, 15 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Models and Methods
  4. Long Short-Term Memory Neural Network (LSTM)
  5. Next Generation Reservoir Computing (NGRC)
  6. Simulation and Results
  7. Dataset Generation
  8. Lorenz System
  9. Rössler System
  10. Chen System
  11. Qi System
  12. Task 1: Multi-steps forecasting of chaotic system behavior
  13. Task 2: Predicting System State With Noisy Input Data
  14. Conclusion

Figures (15)

  • Figure 1: The LSTM cell's structure
  • Figure 2: Schematic representation of the reservoir computing framework.
  • Figure 3: Schematic representation of the NGRC framework.
  • Figure 4: Four representative chaotic systems a) Lorenz System b) Rössler System c) Chen System d) Qi System
  • Figure 5: Comparation of 3 methods' prediction results
  • ...and 10 more figures