Coplanar cracks in pipeline girth welds, under the combined action of internal pressure and axial tensile load, may interact with each other, significantly increasing the risk of pipeline failure. To rapidly and accurately predict the driving force of such crack groups, a physics-informed neural network (PINN) model is constructed by incorporating the monotonic relationships between the crack driving force and both the crack dimensions and the external loads. The finite element method is employed to simulate the mechanical behavior of circumferential coplanar cracks in pipeline girth welds subjected to internal pressure and external axial load. Samples for training and validation of the PINN model are generated using Latin hypercube sampling (LHS), followed by model training and prediction. The results show that, compared with the traditional artificial neural network (ANN), the PINN model incorporating physical constraints exhibits significant advantages in both prediction accuracy and generalization capability, enabling effective evaluation of the driving force of interacting cracks in girth welds under various working conditions. Based on this model, the influence of material mechanical properties and weld geometric parameters on crack behavior is further explored. The study finds that an increase in the strength mismatch parameter reduces the crack driving force. In under?matching conditions, increasing the groove angle and the relative width of the root weld zone elevates the crack driving force, while an opposite trend is observed under over?matching conditions. When the crack spacing is small, an increase in the mismatch parameter enhances crack interaction; this effect becomes negligible when the spacing is large, and the weld geometric parameters have no significant influence on crack interaction. In addition, an assessment of the crack combination method with the empirical formula reveals that its conservatism rises steadily as the strength mismatch parameter shifts from under-match to over-match. Consequently, the evaluation results transition gradually from a non-conservative to a conservative state. The accuracy of this method can be improved by reasonably modifying the crack driving force calculation formula. A more reliable analytical tool and theoretical reference for the structural safety assessment of defective pipelines is provided in this study.