Physics-Informed Deep Recurrent Back-Projection Network for Tunnel Propagation Modeling

Accurate and efficient modeling of radio wave propagation in railway tunnels is is critical for ensuring reliable communication-based train control (CBTC) systems. Fine-grid parabolic wave equation (PWE) solvers provide high-fidelity field predictions but are computationally expensive for large-scale tunnels, whereas coarse-grid models lose essential modal and geometric details. To address this challenge, we propose a physics-informed recurrent back-projection propagation network (PRBPN) that reconstructs fine-resolution received-signal-strength (RSS) fields from coarse PWE slices. The network integrates multi-slice temporal fusion with an iterative projection/back-projection mechanism that enforces physical consistency and avoids any pre-upsampling stage, resulting in strong data efficiency and improved generalization. Simulations across four tunnel cross-section geometries and four frequencies show that the proposed PRBPN closely tracks fine-mesh PWE references. Engineering-level validation on the Massif Central tunnel in France further confirms robustness in data-scarce scenarios, trained with only a few paired coarse/fine RSS. These results indicate that the proposed PRBPN can substantially reduce reliance on computationally intensive fine-grid solvers while maintaining high-fidelity tunnel propagation predictions.