Date of Publication :20th November 2023

Abstract: Time series prediction, particularly for nonlinear dynamical systems, has long been a topic of interest in applied mathematics. Traditional algorithms, encompassing methods such as Linear Regression, Polynomial Regression, and Random Forest, have been utilized for their simplicity and ease of interpretation. While effective in certain scenarios, these traditional models sometimes fall short of capturing the nuanced complexities and longer-term intricacies of dynamic systems. With the recent advancements in artificial intelligence, deep learning methods, notably Gated Recurrent Units (GRU) and Long Short-Term Memory Networks (LSTM), offer promising avenues for enhancing predictive performance. In this study, we evaluate the capabilities of traditional prediction models against the prowess of deep learning techniques using synthetic datasets derived from the renowned Lorenz system. The aim is to determine the efficacy of each model in accurately forecasting time series data, bearing the intricacies of the Lorenz system in mind. Our results shed light on a notable hierarchy in prediction performance. The GRU architecture emerged as the front-runner with an RMSE of 0.21, demonstrating its superior ability to learn and predict the intricate dynamics of the Lorenz system. This was closely followed by the LSTM, yielding an RMSE of 0.29. Among traditional methods, Random Forest and Linear Regression showed comparable performances with RMSEs of 0.48 and 0.51, respectively, while Polynomial Regression trailed with an RMSE of 0.69. This comparative analysis shows that while traditional models hold their ground, deep learning methods, particularly GRU, offer enhanced predictive capabilities for complex dynamical systems. This research underscores the potential of integrating deep learning into time series forecasting and highlights the necessity of choosing the right model based on the intricacy and nature of the data in question.

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