Feedback Long Short-Term Memory: A Long Short-Term Memory-Based Framework for Multivariate Time Series Prediction in Chaotic Systems
نویسندگان
1 Department of Basic Sciences, Technical and Vocational University (TVU), Tehran, Iran
2 Department of Mathematics, Aarhus University, Denmark.
doi
10.30473/coam.2025.72730.1312چکیده
The prediction of chaotic time series is essential for understanding highly nonlinear and sensitive systems, with the Lorenz system serving as a standard benchmark due to its intricate and non-periodic dynamics. Classical forecasting approaches often struggle to capture such irregularities, motivating a shift toward deep learning–based strategies. In this study, we develop two hybrid models—Feedback Long Short-Term Memory (FB-LSTM) and Feedback Variational Stacked LSTM (FBVS-LSTM), specifically designed for multivariate prediction of the Lorenz system. By embedding feedback structures into LSTM networks, the proposed methods deliver enhanced short-term prediction performance without substantial computational costs. Comparative simulations indicate that our frameworks surpass traditional RNNs and baseline LSTM models, achieving prediction accuracies up to 94%. These findings indicate that feedback-enhanced architectures offer effective and practical tools for forecasting chaotic systems, with potential applications in both scientific research and engineering practice.
