Classification of solid and liquid structures using a deep neural network unveils origin of dynamical heterogeneities in supercooled liquids

As the temperature decreases, the dynamics of supercooled liquids significantly slow down and become increasingly heterogeneous in space. Many previous studies have found that static structures also become heterogeneous and are spatially correlated with the dynamical heterogeneity. However, there are still debates on whether the dynamical heterogeneity is controlled by the structures, and which structural order parameters should be used to describe the structural heterogeneities (if exist) in amorphous systems. The appropriate order parameter depends on the specific details of the system and needs to be determined for each system. To address this difficulty, here, we use a machine-learning-based method that was trained solely by the static structures. This method combines convolutional neural networks and gradient-weighted class activation mapping, providing interpretable characteristic structures, which can quantify the degrees of liquid-like and solid-like structures in every local part of the system. We apply this method to a canonical glass-forming system and demonstrate that particles in the liquid-like structures are mobile, while those in the solid-like structures are immobile. The present work develops a novel approach to accurately characterize amorphous structures, which will be particularly useful for systems where appropriate structural order parameters have not yet been identified.