In materials processing (e.g., heat treatment and plastic forming), microscale deformation mechanisms such as dynamic recrystallization (DRX [1]) drive continual grain-structure evolution and redistribution, which in turn alters the overall geometry and governs the mechanical performance of the material. Grain nucleation and growth, together with dislocation activity, induce pronounced topological changes and are often accompanied by strong evolution of anisotropy, nonlinearity, and uncertainty. To analyze and predict microstructural (grain) evolution, experimental characterization techniques such as in-situ microscopy [2] are often limited to a posteriori and offer only partial access to transient dynamics. Classical physics-based simulations, such as phase-field modeling [1], are computationally intensive and typically must be rerun for each case study or parameter setting. To address these limitations, we develop a mechanics-guided machine learning framework based on Graph Neural Cellular Automata (GNCA [3]) to emulate grain evolution. We represent evolution as a sequence of discrete snapshots governed by action-based update rules and encode the process via a least-action formulation that naturally captures topological changes without expensive meshing or remeshing required by traditional numerical methods. The framework can also be readily integrated with experimental data through additional loss terms. To impose equivariance during learning and inference, we incorporate Equivariant Graph Neural Networks (EGNN [4]) into GNCA [3], resulting in an equivariant GNCA (E-GNCA), along with further improvements to be presented. The proposed framework is validated on a series of benchmark problems, and the results demonstrate that it can predict grain structural evolution in a more efficient and robust way than traditional approaches.