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

Mirzajani, Saeed; Roohi, Majid

doi:10.30473/coam.2025.72730.1312

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	Feedback Long Short-Term Memory‎: ‎A Long Short-Term Memory-Based Framework for Multivariate Time Series Prediction in Chaotic Systems
Control and Optimization in Applied Mathematics
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 01 آبان 1404 اصل مقاله (1.55 M)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.30473/coam.2025.72730.1312
نویسندگان
Saeed Mirzajani^* ¹؛ Majid Roohi²
¹Department of Basic Sciences‎, ‎Technical and Vocational University (TVU)‎, ‎Tehran‎, ‎Iran
²Department of Mathematics‎, ‎Aarhus University‎‎, ‎Denmark‎.
چکیده
‎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.
تازه های تحقیق
Introduce two novel hybrid architectures, FB-LSTM and FBVS-LSTM, which embed feedback mechanisms into LSTM networks to enhance short-term predictions of chaotic Lorenz systems while maintaining low computational overhead. Specifically designed for multivariate inputs, these models capture inter-variable dependencies and the nonlinear dynamics characteristic of the Lorenz system, enabling robust short-horizon forecasts. Demonstrate strong predictive performance, achieving up to 94% accuracy in forecasting chaotic trajectories, surpassing traditional RNNs and baseline LSTM architectures without prohibitive computational costs. Exploit the Lorenz system’s intrinsic sensitivity to initial conditions to achieve accurate short-range predictions, reducing the need for long-range forecasting and aligning model focus with the regime where chaotic systems are most predictable. Provide a simple yet powerful alternative to conventional deep learning approaches for continuous chaotic systems, highlighting improvements in performance, interpretability (via decay and missing-rate mechanisms), and practicality for real-world applications. The FBVS-LSTM framework adds decay processes and variable-specific missing-rate considerations, boosting both predictive accuracy and interpretability in chaotic environments. Emphasize that the proposed methods deliver strong predictive performance with reduced computational demands, supporting suitability for larger-scale or real-time applications. The methodology anticipates and addresses missing data through variable-specific mechanisms, indicating resilience in practical, noisy data scenarios.
کلیدواژه‌ها
Deep learning؛ Lorenz system؛ Neural networks؛ Time-series forecasting؛ Global convergence؛ Multivariate sequence prediction

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