Time series forecasting enhanced by Lyapunov exponent via attention mechanism

Autor(es)

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

• Tipo de documento: Artigo Científico
• Fonte: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS; v. 678, p. 30-pg., 2025-09-06.

Resumo

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 stateof-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. (AU)

• Processo FAPESP: 24/01245-1 - Aprendizado auto-supervisionado guiado por transformadas baseadas em caos no auxílio ao diagnóstico do Carcinoma de Pulmão
• Beneficiário: Joao Batista Florindo
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 20/09838-0 - BI0S - Brazilian Institute of Data Science
• Beneficiário: João Marcos Travassos Romano
• Modalidade de apoio: Auxílio à Pesquisa - Programa Centros de Pesquisa Aplicada