Latent-Space Learning of Phase-Ordering Dynamics with Autoencoders

Phase-ordering dynamics provides a fundamental framework for understanding how long-range order and complex patterns emerge following symmetry breaking in nonequilibrium systems. The coarsening of ordered domains is typically governed by universal scaling laws, such as the power-law growth of characteristic length scales with time. Here we explore whether such universal behaviors can be identified and represented by machine-learning models. In particular, we examine whether the essential physics of phase ordering can be encoded within the latent space of an autoencoder trained on simulation data. As a concrete example, we consider the coarsening dynamics of a nonconserved Ising order parameter, which obeys the well-known Allen–Cahn growth law. Interestingly, while the Allen–Cahn dynamics does not manifest explicitly in the latent-space evolution, it is captured within a small subset of latent variables. These findings highlight the potential of machine-learning models for uncovering reduced representations and hidden structure in nonequilibrium physical dynamics.