Geometry-sensitive surface pressure response and rapid deep neural operator prediction for high-speed trains under crosswinds

Crosswind-induced surface pressure on high-speed trains is affected by yaw angle, local surface orientation, curvature variation, and streamwise flow development, while conventional computational fluid dynamics (CFD) remains costly for aerodynamic assessment in complex crosswind environments. This study proposes a geometry-enhanced Deep Operator Network (DeepONet) to reconstruct the surface pressure response of trains influenced by local geometry under crosswinds. In this network, the branch network is used to encode the relative incoming-flow state, whereas the trunk network is used to characterize local geometric effects. Results show that large pressure gradients and local prediction errors are mainly concentrated in regions with abrupt geometric variations, indicating the sensitivity of crosswind pressure response to local geometry. As the yaw angle increases, the windward high-pressure region of the head car expands, the roof and leeward-side suction regions strengthen, and pressure recovery with flow separation near the tail car generates a side force component opposite to that of the head car. The model reconstructs unseen crosswind pressure fields, with coefficient of determination (R2) values of 0.94–0.95 in the crosswind-sensitive nose-tip region of the head car. Aerodynamic loads integrated from the predicted pressure follow the CFD trends, and the R2 values of rolling moment coefficients exceed 0.99 in most regions. Compared with the baseline DeepONet, geometry-enhanced features reduce localized high-error bands near abrupt geometric transitions. The single-condition prediction time is 42.3 s, giving a speedup of approximately 1957 relative to CFD. This model provides a useful reference for rapid train-surface pressure prediction under crosswinds.