In this project, we tried to implement S. Pourmohammad Azizi research "2DS-L: A dynamical system decomposition of signal approach to learning with application in time series prediction" https://doi.org/10.1016/j.physd.2024.134203

@article{AZIZI2024134203, title = {2DS-L: A dynamical system decomposition of signal approach to learning with application in time series prediction}, journal = {Physica D: Nonlinear Phenomena}, volume = {465}, pages = {134203}, year = {2024}, issn = {0167-2789}, doi = {https://doi.org/10.1016/j.physd.2024.134203}, url = {https://www.sciencedirect.com/science/article/pii/S0167278924001544}, author = {S. Pourmohammad Azizi}, keywords = {Dynamical system, Signal decomposition, Time series, Long short-term memory, Gated recurrent unit, Neural network}, abstract = {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.} }