In recent years, Iran has faced natural gas shortages during the cold months due to peak demand on cold days and the lack of sufficient imports or storage, making inventory management of gas transmission pipelines a critical solution. Simulating the dynamic behavior of such systems is often time-consuming and costly due to the complexity of interactions among their components. In this study, a data-driven surrogate model based on a Nonlinear Autoregressive Neural Network with eXogenous Inputs (NARX) is developed to analyze and predict the behavior of natural gas transmission networks under peak demand conditions. The quasi-experimental data required for training the NARX model were generated through dynamic simulation of a quasi-real unit in Aspen HYSYS, and the model was trained using the Levenberg–Marquardt algorithm. To evaluate the model’s performance, the Mean Absolute Error (MAE), Mean Squared Error (MSE) and Coefficient of Determination (R²) were calculated on both training and test datasets. The results show that on the test data, the model achieved MAE = 0.01474, MSE = 0.002229, and R² = 0.9968. Compared to full dynamic simulation, the proposed surrogate model is approximately 1133 times faster, corresponding to a 99.911% reduction in computation time, while maintaining high accuracy. This unique combination of speed and precision enables real-time analysis and decision-support applications during peak-demand scenarios, positioning the proposed NARX-based model as an efficient and reliable tool for forecasting and peak-shaving management in natural gas transmission networks.