A Generalizable Physics-Informed Long-Range Attentive Network for Radio Wave Propagation Modeling in Tunnels

Accurate and efficient modeling of radio wave propagation in tunnel environments is critical for the deployment and optimization of modern intelligent transportation systems (ITSs). Traditional physics-based methods, such as the parabolic wave equation (PWE) methods, face significant challenges due to their high computational cost. Recently, the adoption of machine learning (ML) methods has enabled rapid modeling of radio wave propagation in tunnels. However, these approaches face significant challenges in accurately predicting long-range propagation in tunnel environments, limiting their practical applicability. This article proposes a physics-informed long-range attentive propagation network (PLAPN) that combines convolutional feature encoding, a dual-path attention translator, and a sliding window inference strategy. The model is designed to directly learn received signal strength (RSS) distributions from short-range simulations in tunnels, enabling long-range sequence prediction while capturing both spatial and temporal dependencies. Meanwhile, we introduce a sliding window strategy that substantially enhances prediction accuracy by focusing attention on local temporal contexts and reducing error accumulation over long sequences. Both measurement data obtained from the Massif Central tunnel and simulation results across diverse tunnel geometries and frequency settings confirm that the windowed version of the model (PLAPN-Win) delivers superior reconstruction accuracy compared to its nonwindowed variant (PLAPN-Nowin) and a conventional convolutional neural network (CNN) baseline.