Graft copolymers are widely used as compatibilizers in homopolymer blends. Computational modeling techniques for predicting the compatibilization efficiency of such polymeric materials have substantially accelerated their development. We employ an efficient particle-based simulation method, namely dissipative particle dynamics (DPD), to systematically investigate the compatibilization efficiency of graft copolymers for a wide range of design parameters such as polymer chemistry, backbone and side chain lengths, and the number of side chains. We find that regular graft copolymers (with regular side chain distribution) exhibit different compatibilization efficiencies at the same areal concentrations. This indicates that the molecular architecture plays a critical role in their compatibilization efficiency. To understand these observations, detailed analysis has been performed. Specifically, the relative shape anisometry of the graft copolymers, which is defined as the ratio of their gyration tensor elements in directions normal and parallel to the surface, is found to be strongly correlated to their compatibilization efficiency. Furthermore, we have investigated three specific graft copolymer types, namely, double-end-grafted (side chains concentrated near both chain ends of the backbone), mid-grafted (side chains concentrated on the center of the backbone), and single-end-grafted (side chains only concentrated near one end of the backbone), to understand the influence of varying side chain distributions. Compared to all other series, the mid-grafted copolymers exhibit the best compatibilization efficiency. Combining the obtained DPD results with five models of machine learning (ML), including linear regression (LR), elastic net (EN), random forest (RF), extra tree (ET), and gradient boosting (GB), provides effective predictions for the compatibilization efficiency. The GB model, which yields the best accuracy, has been further used to acquire the feature importance rank (FIR). Starting from these ML models and the FIR analysis, we have developed a framework for fast predictions of the compatibilization efficiency of graft copolymers. This novel framework utilizes physical insights into effects of material properties, such as chemistries and molecular architectures, on the compatibilization efficiency of graft copolymers and paves the way for advanced design of polymer compatibilizers.