High-speed rail passenger flow prediction based on crossformer and quantile regression: A deep learning approach assisted by internet search indices

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Understanding potential fluctuations in passenger volume is crucial for the operation and management of high-speed rail, especially during peak times. The uncertainty caused by multiple factors is the main obstacle to accurate prediction. To quantify and mitigate the impact of these uncertainties, Internet search indices are utilized as insightful resources to grasp dynamic trends in passenger flow. Leveraging minimum redundancy maximum relevance, we identify the top search index features based on their predictive contribution to high-speed rail passenger flow. A two-level decomposition strategy is then established based on variational modal decomposition to extract significant influencing factors hidden in the Internet index and capture the dynamic uncertainty of passenger flow. By integrating Crossformer with quantile regression, we construct the upper and lower bounds of the prediction interval. Furthermore, the obtained upper and lower bounds are corrected by the error of point prediction, which allows for dynamic adjustment of the prediction intervals width based on fluctuations in uncertainty, thereby refining the precision of the prediction interval. Finally, the developed approaches effectiveness is validated through two real-world experiments, and the experimental results indicate that this method can more accurately capture variations in high-speed rail passenger flow, improving both management and service quality.