Spatio-Sequential Recurrent Network for 3-D Tunnel Propagation Modeling

Abstract

Fine-mesh parabolic wave equation (PWE) simulations are high-fidelity but time-consuming, which limits real-time tunnel propagation analysis and motivates coarse-to-fine reconstruction. Existing machine learning (ML)-assisted tunnel models typically provide only one-dimensional (1-D) longitudinal refinement or two-dimensional (2-D) cross-sectional refinement, rather than joint 3-D enhancement. Motivated by this gap, this letter proposes a U-shaped gated spatio-sequential recurrent neural network (UG-SSRNN), a spatio-sequential reconstruction model for tunnel electromagnetic fields. UG-SSRNN jointly super-resolves transverse slices and models longitudinal evolution. It uses sliding-window context encoding and a K-layer convolutional recurrent backbone with a shared propagation-context state and diagonal feedback. A prediction-aware upsampling head leverages the previous prediction to improve slice-to-slice consistency. Experiments on four tunnel cross sections, unseen-material and unseen-frequency tests, and validation in the Massif Central tunnel show close agreement with fine-mesh PWE references. The proposed approach significantly reduces tunnel electromagnetic modeling time.