Jaiswal, Prabhat Kumar

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. © 2025 Author(s).

The study of glass-forming systems with pinning has provided significant insight into the complex dynamics of glasses. Among various approaches, particle pinning has emerged as a powerful method to probe dynamical heterogeneity and slow relaxation in supercooled liquids. Although most studies focus on random pinning protocols, the impact of pinning in lower-dimensional systems remains underexplored. We investigate the dynamical properties of a two-dimensional binary Kob-Andersen glass interacting through a modified Mie ( n , 6 ) potential with varying repulsive ranges, using a template pinning protocol. For a fixed pinning concentration, our results on mean-squared displacements and self-diffusion coefficients indicate enhanced mobility of particles with an increase in softness of the repulsive core of the interaction potential. However, an increase in particle pinning hinders the particle mobility and amplifies the caging effect across these systems. Notably, the inverse temperature dependence of both the self-diffusion coefficient and the relaxation time for varying pinning concentrations collapses onto a universal curve when scaled by a characteristic temperature, defined as the temperature at which the self-diffusion coefficient approaches zero. At a fixed range of repulsive interaction, both the non-Gaussian parameter and the Stokes-Einstein violation increase with pinning concentration, indicating enhanced dynamic heterogeneity. However, at a fixed pinning fraction, these indicators show distinct trends with interaction range, reflecting the complex nature of dynamical heterogeneity. Our results offer insights into the role of concentration of pinned particles and the range of repulsive interactions in controlling the glass transition, with potential applications in designing disordered materials with desired transport properties. © 2025 Author(s).