To address the challenges of fracture-vuggy parameter prediction in carbonate reservoirs, such as strong multi-scale heterogeneity and a lack of physical constraints, this study proposed a Transformer–Graph Neural Operator (GNO)–Physics-Informed Neural Network (PINN) joint prediction framework, which achieves a bidirectional coupling between multi-source data fusion and physical laws. First, a Transformer module with a multi-scale attention mechanism and spherical coordinate effectively captures cross-scale spatiotemporal features in three-dimensional geological space (reducing error by 12.3%). Second, a dynamic GNO based on physical similarity adaptively tracks the evolution of fracture-vuggy connectivity (achieving a topology update accuracy of 93.5%). Finally, a PINN module embedded in the seepage-mechanical coupling equations constrains the physical residual loss to the order of 0.42×10⁻3, reducing the conservation error from 3.17% to 0.48%. In an empirical study of Ordovician fracture-vuggy reservoirs in the Tarim Basin, this framework achieved a mean absolute error of 3.57% and an R2 of 0.90 for fracture-vuggy volume fraction (Vf). In high-pressure gradient regions (>5 MPa/m), the relative error was reduced by 18%, significantly outperforming traditional methods (reducing Kriging error by 40.7%) and single-module models (PINN error reduction of 15.3%). Experimental results showed that dynamic graph construction increased the spatial autocorrelation index (Moran’s I) to 0.71; the introduction of physical constraints reduced extreme error samples by 63%; and the multimodal collaborative training strategy resulted in a 19.7% improvement in overall performance. This research provides a new paradigm for high-precision and physically interpretable digital twin modeling of carbonate reservoirs.