混沌时间序列预测算法研究

Research on Chaotic Time Series Prediction Algorithms

摘要: 混沌现象在自然界的各种动态系统中广泛存在，例如天气模式、流体湍流和生物神经信号传递。由于这些系统的复杂性，通常无法获得精确的数学模型，且只能获得可观测的时间序列数据。因此，利用已知的时间序列数据预测未来的系统行为至关重要。本文提出了一种结合时序卷积网络(TCN)的长短时记忆网络，旨在重构的相空间中进行混沌时间序列的预测。我们使用连续与离散动力系统生成的数据集，经过将长短时记忆网络(TCN-LSTM)与其他四种预测模型(TCN、LSTM、MLP和SVR)进行了对比实验。实验结果表明，TCN-LSTM模型的预测能力要优于其他模型，具体表现为均方根误差(RMSE)和平均绝对误差(MAE)最接近0，而决定系数(R²)最接近1。结果表明，TCN能有效提取重构相空间中的空间特征，而LSTM能够充分捕捉时间序列中的长期依赖关系，从而实现了更为准确的预测。

Abstract: Chaotic phenomena are widely present in various dynamic systems in nature, such as weather patterns, fluid turbulence, and biological neural signal transmission. Due to the complexity of these systems, it is often impossible to obtain precise mathematical models, and only observable time series data can be acquired. Therefore, predicting the future behavior of the system using known time series data is crucial. This paper proposes a chaotic time series prediction method that combines the Temporal Convolutional Network (TCN) with Long Short-Term Memory (LSTM) networks, aiming to predict chaotic time series in the reconstructed phase space. We use datasets generated by continuous and discrete dynamical systems and compare the performance of the TCN-LSTM model with four other prediction models (TCN, LSTM, MLP, and SVR). The experimental results show that the TCN-LSTM model outperforms the other models, with Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) values closest to zero, while the coefficient of determination (R²) is the closest to one. The results indicate that TCN effectively extracts spatial features in the reconstructed phase space, while LSTM captures long-term dependencies in the time series, enabling more accurate predictions.