2DS-L: A dynamical system decomposition of signal approach to learning with application in time series prediction

• Published in: Physica. D 2024-09, Vol.465, p.134203, Article 134203
• Main Author: Azizi, S. Pourmohammad
• Format: Article
• Language: English
• Subjects: Dynamical system; Gated recurrent unit; Long short-term memory; Neural network; Signal decomposition; Time series
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2024.134203

In this research, we propose a novel approach for time series forecasting using dynamical systems, signal processing, and Neural Networks, which we named 2DS-L. As dynamical systems frequently display complex and nonlinear behavior, accurately modeling time series data’s evolving dynamics and interdependencies is crucial to time series prediction. Managing high-dimensional and complex datasets is another challenge in machine learning time series prediction. Using mathematical relationships, the proposed method decomposes the time series signal and establishes a connection between its dynamical system and a neural network. The performance of the 2DS-L method was compared with other popular methods like LSTM, GRU, and DEANN using stock price data, climate change data, and biology data. The results showed that despite having only 35% of the training parameters of LSTM and 50% GRU, the 2DS-L method’s performance was better or close to it. This paper’s approach offers an efficient and accurate forecasting technique that could be valuable in various domains, including finance, climate, and biology. •Introduced 2DS-L for time series forecasting using dynamical systems, signal processing, and neural networks.•2DS-L efficiently trains by decomposing signals and connecting the dynamical system to a neural network.•Experimentally proven superior or comparable forecasting accuracy to LSTM, GRU, and DEANN.•Versatile application across finance, climate, and biology domains.