Graph neural network for prediction of phase-ordering kinetics

The study of evolving structures and patterns has always been a central point in understanding the universe, ranging from molecular processes at the nanoscale to the galaxies. Recent approaches have adopted machine learning techniques to study these dynamical systems. Here, we implemented the graph neural network to predict the spatiotemporal pattern formation in the ordering of a ferromagnet (nonconserved system) and phase separation of a binary mixture (conserved system). We show that our model can predict the evolution of the nonconserved system with good accuracy. However, prediction for the conserved system fails to preserve the conservation of the order parameter. Furthermore, we find that the prediction for the domain coarsening characterized by a single length scale is consistent with the Allen-Cahn growth law for ferromagnetic ordering. In contrast, we observe deviation from the Lifshitz-Slyozov growth law for the phase-separating binary mixture. Beyond the Ising ferromagnet and binary alloys, our model could be applied to the evolution of other nonequilibrium phenomena, such as surface-directed spinoidal decomposition and percolation.