Document Type : Research Article
Authors
1 Department of Basic Sciences, Technical and Vocational University (TVU), Tehran, Iran
2 Department of Mathematics, Aarhus University, Denmark.
10.30473/coam.2025.72730.1312
Abstract
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.
Highlights
- 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.
Keywords
- Deep learning
- Lorenz system
- Neural networks
- Time-series forecasting
- Global convergence
- Multivariate sequence prediction
Main Subjects
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