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<p>Accurate prediction of chaotic time series is essential across fields such as healthcare and engineering, where reliable forecasting of complex systems is required. This paper proposes two novel deep learning models that utilize recurrence plots (RPs) as representations of reconstructed phase space (RPS) to enhance prediction accuracy. The first model, ForCNN-LSTM, combines convolutional neural networks with long short-term memory networks to capture both spatial and temporal dynamics from augmented RPs of time series embedded in the RPS, where additional quantitative information is added to the images. The second model, a multimodal hybrid network (MHN), processes raw time series and RPs in parallel, merging outputs through fully connected layers to improve predictive capabilities. We evaluate both models on chaotic systems generated from Lorenz, Rössler, and Lorenz-like equations, as well as on real electrocardiogram data from arrhythmia dataset. The results show that the proposed MHN model achieves a lowest RMSE for both a one-step prediction horizon and a ten-step prediction horizon. Additionally, the model using only RPs as input outperformed the baseline models in multi-step prediction. Therefore, the combination of spatial and temporal feature extraction enhances chaotic time series analysis, opening new possibilities for accurate predictions in dynamic systems.</p>

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Chaotic time series prediction using combination of spatial and temporal information by deep learning approaches

  • 期刊论文

  • 发表日期：

    2025年3月27日

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  • Helia Khoshroo,
  • Yasser Shekofteh

摘要

Accurate prediction of chaotic time series is essential across fields such as healthcare and engineering, where reliable forecasting of complex systems is required. This paper proposes two novel deep learning models that utilize recurrence plots (RPs) as representations of reconstructed phase space (RPS) to enhance prediction accuracy. The first model, ForCNN-LSTM, combines convolutional neural networks with long short-term memory networks to capture both spatial and temporal dynamics from augmented RPs of time series embedded in the RPS, where additional quantitative information is added to the images. The second model, a multimodal hybrid network (MHN), processes raw time series and RPs in parallel, merging outputs through fully connected layers to improve predictive capabilities. We evaluate both models on chaotic systems generated from Lorenz, Rössler, and Lorenz-like equations, as well as on real electrocardiogram data from arrhythmia dataset. The results show that the proposed MHN model achieves a lowest RMSE for both a one-step prediction horizon and a ten-step prediction horizon. Additionally, the model using only RPs as input outperformed the baseline models in multi-step prediction. Therefore, the combination of spatial and temporal feature extraction enhances chaotic time series analysis, opening new possibilities for accurate predictions in dynamic systems.