Abstract: Aiming at the challenge of non-destructive testing for sidewall root penetration depth in ultra-narrow gap arc welding, a hybrid prediction model integrating mechanism-driven and data-driven approaches was proposed. Firstly, a mechanism-based main model was established by integrating thermal balance principles and weld cross-sectional area modeling to predict baseline values of sidewall root penetration. Secondly, a PSO-LSTM error compensation model was developed using particle swarm optimization（PSO） to optimize hyperparameters of the long short-term memory（LSTM）network, aiming to predict errors from the mechanism-based main model. Finally, the ultimate hybrid prediction results were obtained by superimposing baseline values with error predictions. The results demonstrate that the hybrid model achieves lower mean squared error（0.0152） and mean absolute error（0.0914） compared with the single mechanism-based model.Comparative analysis confirms that the PSO-LSTM compensation model exhibits stronger error correction capability for the mechanism-based main model. The validation through rail welding applications shows that the hybrid prediction model can be practically applied for non-destructive testing of sidewall root penetration in rail welds, laying the foundation for quality assessment and control in ultra-narrow gap welding.