## 5 Future Research Prospects  
Subway passenger flow prediction is inherently challenging due to the influence of multiple dynamic factors. Building on the limitations discussed earlier, future research will prioritize expanding the scope and depth of the model to enhance its predictive accuracy and robustness. A key focus will be integrating additional data sources, such as weather conditions, holidays, large-scale events, and detailed subway network information, to capture a more comprehensive range of influencing factors. These diverse data sources will be incorporated as covariates in the model, enabling it to account for dynamic environmental changes and improving its capacity to predict passenger flow effectively. Another limitation of the current study is the fixed use of a 5 min time interval for data aggregation. While this interval was chosen to balance data granularity and noise, it is critical to explore the impact of alternative time intervals, such as 4 or 6 min, on model performance. This exploration will determine whether varying time intervals can reveal additional insights into system dynamics, particularly in terms of chaotic behavior and short-term seasonal patterns. Specifically, we aim to investigate how these intervals affect the detection of chaotic attractors and prediction accuracy during critical periods like rush hours. Given that our study addresses a chaotic system characterized by a positive Lyapunov exponent, it is essential to clarify how accurate predictions are achieved despite the inherent unpredictability of chaos. A positive Lyapunov exponent indicates a sensitive dependence on initial conditions, leading to the exponential divergence of trajectories and making long-term predictions particularly challenging. However, the model's strong short-term predictive performance can be attributed to the limited predictability retained by chaotic systems over short time frames. To leverage this, we employ machine learning models capable of capturing short-term patterns and correlations in the data before chaotic divergence becomes significant. By utilizing local stability, the model extracts meaningful yet transient insights from the system's dynamic behavior. Future research will further refine the conditions under which these short-term predictions remain reliable and extend the predictive horizon wherever possible. This will involve enhancing preprocessing techniques, refining decomposition methods, and developing chaos-aware model architectures capable of managing chaotic divergence more effectively. Additionally, hybrid approaches that combine traditional statistical models with machine learning techniques will be explored to deepen the understanding and mitigate the limitations imposed by chaotic dynamics. The computational complexity of the proposed hybrid model presents another challenge. To address this, future research will focus on optimizing the model architecture and exploring more efficient machine learning algorithms to reduce complexity without compromising performance. Furthermore, the current dataset, limited to a single city's subway network, raises concerns about the model's generalizability. To validate the approach across diverse urban contexts, we plan to extend the model to metro networks with different structural and passenger flow characteristics, incorporating data from major systems such as those in Beijing, London, and Shanghai. Ultimately, the goal is to develop a comprehensive, dynamic prediction framework that integrates various models. By leveraging the strengths of these models, we aim to provide a holistic approach to managing urban metro systems, enabling operators to make real-time operational adjustments and informed long-term strategic decisions. This integrated approach is expected to enhance resource allocation, optimize passenger transfers, and reduce congestion, contributing to more efficient, reliable, and sustainable urban transportation systems.