Feedback Long Short-Term Memory:A Long Short-Term MemoryBased 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 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.