Time series forecasting enhanced by Lyapunov exponent via attention mechanism

Reneé Rodrigues Lima, Jerson Leite Alves, Francisco Alves dos Santos, Davi Wanderley Misturini and Joao B. Florindo

Physica A: Statistical Mechanics and its Applications, 2025, vol. 678, issue C

Abstract: 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.

Keywords: Deep neural network; Lyapunov exponent; Time series forecasting; Attention mechanism (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437125006004
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:678:y:2025:i:c:s0378437125006004

DOI: 10.1016/j.physa.2025.130948

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().