Feedback Long Short-Term Memory‎: ‎A Long Short-Term Memory-Based Framework for Multivariate Time Series Prediction in Chaotic Systems

‎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 ۹۴%‎. ‎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.

کلیدواژه ها:

deep learning ، Lorenz system ، Neural networks ، Time-series forecasting ، Global convergence ، Multivariate sequence prediction