Time series forecasting enhanced by Lyapunov exponent via attention mechanism

This paper proposes a novel time series forecasting approach that integrates chaos theory and deep learning. By computing local Lyapunov exponents over a sliding window, we extract the dynamic structure of the time series and inject this information into deep models via a self-attention mechanism. This enriched representation enhances the model’s ability to capture nonlinear and “quasi-chaotic” patterns. We apply our method to three deep learning architectures (N-BEATS, LSTM, and GRU), comparing their standard and chaotic-aware versions across seven datasets—one synthetic and six real-world datasets from finance, energy, traffic, and climate domains. Experimental results show that our approach improves forecasting accuracy by an average of 28.0% over traditional deep learning models and 30.8% compared to state-of-the-art methods, according to MAE, RMSE, and MAPE metrics. These findings highlight the potential of combining Lyapunov-based local dynamics and attention mechanisms for robust and interpretable forecasting, especially in complex time series with nonlinear behaviors.