###### Abstract  
Accurate prediction of subgrade temperatures in seasonally frozen regions is crucial for understanding thermal states, frost heave phenomena, stability, and other critical characteristics. This study employs a nonlinear autoregressive with exogenous input (NARX) network to predict short-term subgrade temperatures in the Golmud-Naggu section of China's National Highway 109. The methodology involves preprocessing subgrade monitoring data, including temperature, water content, and frost heave, followed by developing a temperature prediction model. This tailored NARX neural network, compared to the traditional BP neural network, integrates feedback and delay mechanisms for monitoring data, offering superior memory and dynamic response capabilities. The precision of the NARX model is assessed with the backpropagation (BP) network, indicating that the NARX neural network significantly outperforms the BP model in both precision and stability for temperature prediction in seasonally frozen subgrades. These findings suggest that the NARX model is a valuable tool for accurately predicting subgrade temperatures in seasonally frozen regions, offering significant insights for practical engineering applications. 20242  
China holds the third-largest area of frozen ground globally. Frozen soil is categorized by the duration of freezing into three types: permafrost (freeze for two years or more), seasonally frozen soil (freeze for 15 days to two years), and intermittently frozen soil (freeze for less than 15 days annually). Permafrost is predominantly found in high-altitude regions like the Qinghai-Tibet Plateau and high-latitude areas such as the Lesser Khingan, Greater Khingan, and Changbai Mountain, covering approximately one-fifth of China's land area. In contrast, seasonally frozen soil, with shorter freezing periods, surrounds permafrost zones and regions where the monthly minimum temperature dips below 0 \({}^{\circ}\)C, encompassing over half of China's territory [6]. Intermittently frozen soil is mainly found between the Qinling-Huaihe Line and the Lingnan Line [7]. Despite the widespread presence of seasonally frozen soil across China, research on subgrade engineering in these regions remains limited, with a predominant focus on permafrost areas [8]. Seasonal freeze-thaw processes introduce subgrade stability challenges, such as frost heave and thaw settlement, which are influenced by temperature fluctuations [4; 9; 10]. Existing methods for predicting temperature fields in subgrades have primarily relied on numerical simulations [11; 12; 13; 14; 15] and backpropagation (BP) network models [16; 17; 18; 19]. While these methods are beneficial, they struggle to capture the nonlinear and dynamic interactions between temperature, water content, and frost heave in seasonally frozen soils. These traditional models [20; 21] often lack the capability to model these complex dependencies, leading to limited prediction accuracy and applicability in real-world scenarios. Advanced models like the nonlinear autoregressive with exogenous inputs (NARX) network offer potential solutions to these challenges [22]. The NARX network has two distinguishing features. First, its feedback and delay mechanisms enable the model to account for past outputs in current predictions, enhancing memory and allowing the network to capture complex temporal patterns more effectively. Second, the NARX network's flexibility with external inputs enables the integration of exogenous variables, such as water content and frost heave, which are critical for improving temperature prediction accuracy in frozen soils. These characteristics allow the NARX network to address the temporal dependencies and dynamic responses inherent in time-series data, providing robust modeling capabilities. Recently, the NARX network has proven its value in various domains, including weather forecasting [23], energy load forecasting [24], water resources management [25; 26], and environmental monitoring [27].