Machine learning of condensed-matter phases with physical interpretability

Nature displays a vast variety of phase transitions. Detecting and quantifying these often requires creative design of order parameters, which are strongly system dependent. Thanks to recent advances in machine learning (ML), it is now possible to identify phase behavior by directly analyzing atomistic configurations via modern pattern-recognition techniques. Whereas these ML approaches are universal and robust, they often suffer from the lack of physical interpretability. Here we introduce a new ML scheme, which distinguishes different condensed-matter phases by autonomously recognizing order parameters. When applied to two-dimensional Ising models, our method can accurately predict the Curie and Néel temperatures and capture the corresponding critical phenomena by recognizing ferro- and antiferro-magnetizations, respectively. Going beyond these prototypical test cases, we analyze the nonequilibrium polymeric sol–gel transition, locating not only the transition temperature, but also discovering two classes of underlying collective behavior, the condensation and network-formation modes. Compared to existing MLs, our method offers physical insights as well as high training efficiency.