## 5 Discussion  
This study offers valuable insights into the design and maintenance of subgrades in seasonally frozen regions, demonstrating that the NARX network model significantly enhances temperature prediction accuracy. This improvement enables engineers and practitioners to make better-informed decisions, ultimately improving subgrade performance. However, several limitations of the current study warrant consideration.  
Firstly, the temperature prediction model integrates only two types of exogenous inputs: water content and frost heave. While these variables are critical, the environmental factors affecting subgrade temperature are not limited to these two. Other factors such as soil thermal conductivity, moisture content variations, snow cover, and solar radiation can also significantly impact subgrade temperatures. Future models should consider incorporating these additional environmental variables to provide a more comprehensive and accurate prediction framework.  
Secondly, although the current model achieves acceptable accuracy for each subgrade depth, optimizing hyperparameters separately for each depth would yield the most precise results. However, this approach may be impractical due to time and resource demands. A potential solution could involve constructing a multi-output NARX model that predicts temperatures across multiple depths simultaneously by treating each depth as an additional output. Alternatively, transfer learning techniques [47; 48], in which a base model trained on one depth is fine-tuned with minimal adjustments for other depths, may be feasible. Future research will explore these strategies to improve model efficiency and adaptability.  
Thirdly, this study's demonstration is limited to a single subgrade case on the Golmud-Nagqu section of China's National Highway 109. This specific case study provides valuable insights but does not account for the variability in geological and climatic conditions found in other regions. Applying the proposed NARX network model to a broader range of geographic locations with diverse soil types, climatic conditions, and subgrade structures would help validate the model's robustness and versatility.  
Additionally, this study's temporal scope is relatively limited due to data availability, focusing on short-term predictions. Investigating the model's performance over longer prediction horizons poses a higher challenge. Any advance in short-term forecasts would benefit long-term predictions, which are essential for understanding the cumulative effects of freeze-thaw cycles on subgrade stability and performance. Further work should extend the model to include long-term predictions, thereby strengthening the data foun  
Figure 11: Normalized importance proportion of temperature, water content, and frost heave.  
dation for assessing the enduring impacts of freeze-thaw cycles on subgrade integrity and performance.  
Finally, collaborative efforts with field engineers and practitioners are crucial for validating the model's practical utility and integrating it into routine subgrade maintenance and monitoring practices. By addressing these limitations and expanding the scope of research, the NARX network model can become an indispensable tool for engineers working in seasonally frozen regions, leading to more resilient and durable infrastructure.