Machine learning based prediction of phase ordering dynamics

Machine learning has proven exceptionally competent in numerous applications of studying dynamical systems. In this article, we demonstrate the effectiveness of reservoir computing, a famous machine learning architecture, in learning a high-dimensional spatiotemporal pattern. We employ an echo-state network to predict the phase ordering dynamics of 2D binary systems - Ising magnet and binary alloys. Importantly, we emphasize that a single reservoir can be competent enough to process the information from a large number of state variables involved in the specific task at minimal computational training cost. Two significant equations of phase ordering kinetics, the time-dependent Ginzburg-Landau and Cahn-Hilliard-Cook equations, are used to depict the result of numerical simulations. Consideration of systems with both conserved and non-conserved order parameters portrays the scalability of our employed scheme.