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<p>This work presents a systematic framework for chaotic time series forecasting that uniquely conducts a comprehensive comparative study across multiple prediction methods: Point-to-Point (P2P), Nonlinear Autoregressive (NAR), and Sequence-to-Sequence (S2S). While previous studies typically adopt only a single prediction method, this paper offers the unified evaluation that contrasts the performance of them, thereby providing new insights into method suitability under different chaotic systems. These methods are synergistically integrated with different deep learning models: Multilayer Perceptron (MLP), Long Short-Term Memory (LSTM) and Fourier Neural Operator (FNO) to evaluate short-term predictive accuracy and long-term phase-space fidelity. The results demonstrate that for non-delayed chaotic systems, the NAR method with FNO achieves the highest modeling accuracy (90.51%), effectively capturing the attractor structures across different chaotic systems, and the RMSE of short-term prediction is 0.165. In contrast, for time-delayed chaotic systems, the S2S-TD method with FNO achieves the highest modeling accuracy (88.54%) and the best computational efficiency, benefiting from its ability to generate multiple future time steps per iteration, and the RMSE of short-term prediction is 0.443. This work aims to provide important references for chaotic time series forecasting based on neural networks.</p>

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Harnessing deep learning for chaotic time series forecasting: a performance comparison of different methods and models

  • 期刊论文

  • 发表日期：

    2026年1月26日

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  • Lin Jiang,
  • Qixin Wang,
  • Lianshan Yan,
  • Hairong Lin,
  • Xingchen He,
  • Jiacheng Feng,
  • Anlin Yi,
  • Wei Pan

摘要

This work presents a systematic framework for chaotic time series forecasting that uniquely conducts a comprehensive comparative study across multiple prediction methods: Point-to-Point (P2P), Nonlinear Autoregressive (NAR), and Sequence-to-Sequence (S2S). While previous studies typically adopt only a single prediction method, this paper offers the unified evaluation that contrasts the performance of them, thereby providing new insights into method suitability under different chaotic systems. These methods are synergistically integrated with different deep learning models: Multilayer Perceptron (MLP), Long Short-Term Memory (LSTM) and Fourier Neural Operator (FNO) to evaluate short-term predictive accuracy and long-term phase-space fidelity. The results demonstrate that for non-delayed chaotic systems, the NAR method with FNO achieves the highest modeling accuracy (90.51%), effectively capturing the attractor structures across different chaotic systems, and the RMSE of short-term prediction is 0.165. In contrast, for time-delayed chaotic systems, the S2S-TD method with FNO achieves the highest modeling accuracy (88.54%) and the best computational efficiency, benefiting from its ability to generate multiple future time steps per iteration, and the RMSE of short-term prediction is 0.443. This work aims to provide important references for chaotic time series forecasting based on neural networks.