Spatially enhanced physics-informed neural networks for predicting wind speed inside railway windbreak walls

Strong winds pose a major threat to railway operation because their rapid onset and destructive effects can compromise train safety. Most existing warning studies use wind measurements outside windbreak walls, whereas the short-horizon wind conditions inside the protected region remain difficult to estimate. This study proposes a spatially enhanced physics-informed neural network coupled with a long short-term memory network (SE-PINN-LSTM). The model receives a causal 20-step input window comprising observations from three outside measurement points (60 s) and jointly predicts the lateral velocity u at seven inside measurement points one step ahead (3 s). A two-dimensional unsteady RANS formulation with Chen's zero-equation closure is enforced through automatically differentiated continuity and momentum residuals, together with boundary-condition, initial-condition, and physics-data consistency losses. Under a chronological evaluation protocol, the proposed model achieves an average RMSE of 0.3943 m/s and an average relative L 2 error of 0.0895, corresponding to reductions of approximately 13.6% in RMSE and 12.9% in relative L2 error compared with the improved-architecture PINN-LSTM baseline (IA-PINN-LSTM). The results indicate that combining spatial enhancement, temporal modeling, and physics-data coupling provides accurate and physically consistent short-horizon estimates of lateral wind velocity inside the windbreak wall.