Machine Learning and GPU-Accelerated Modeling of Phase Ordering Kinetics

Pattern formation in evolving systems is a fundamental theme across physics, from nanoscale ordering to cosmological structures. The rich dynamics of these nonequilibrium systems are governed by nonlinear evolution equations that couple spatial and temporal degrees of freedom. Since exact solutions are intractable in genral, computational and machine learning methods provide an effective route to study their behavior. We employ a graph neural network (GNN) framework to investigate phase-ordering kinetics in two systems: the ordering of a ferromagnet (nonconserved) and the phase separation of a binary mixture (conserved). The GNN accurately predicts the evolution of the nonconserved system, reproducing domain coarsening consistent with the Allen–Cahn growth law. However, it fails to preserve conservation of order parameter in the binary mixture, leading to deviations from the Lifshitz–Slyozov growth behavior. This highlights the potential of machine learning frameworks for future studies of phase-ordering kinetics and nonequilibrium pattern formation. Further, we also implement GPU-accelerated solvers for the time-dependent Ginzburg–Landau (TDGL) and Cahn–Hilliard–Cook (CHC) equations, achieving substantial computational speedup over traditional CPU-based solvers.