Contents I. Introduction
The rapid growth of communication-based train control (CBTC) systems has highlighted the importance of radio wave propagation characterization in railway tunnels [1], [2], [3], [4], [5]. However, conventional approaches to derive wave propagation models often involve resource-intensive measurement campaigns [6], [7], [8], which can be particularly challenging given the extensive stretch of rail networks spanning tens to hundreds of kilometers. As an alternative, deterministic models based on methods such as vector parabolic equation (VPE) and ray-tracing (RT) [9], [10], [11], [12], [13], have gained popularity. Notably, the VPE method is commonly employed in tunnel environments due to its ability to strike a good balance between accuracy and computational efficiency [14], [15], [16], [17], [18]. Generally, coarse-mesh VPE, characterized by the use of large discretizations in the simulation setup, is fast but yields low-fidelity results, whereas fine-mesh VPE simulations offer higher accuracy but are time-consuming. Nonetheless, substantial computational resources are indispensable to ensure these models deliver the desired accuracy, making them unsuitable for real-time applications [19]. Furthermore, the deployment of CBTC systems requires multiple runs of these models for optimization studies [20], [21], [22], resulting in significant computational expenses.
