Quasicrystals have emerged as the third class of solid-state materials, distinguished from periodic crystals and amorphous solids, that have long-range order without periodicity exhibiting rotational symmetries disallowed for periodic crystals in most cases. The first quasicrystal was discovered by Shechtman in 1984. Over the next 35 years, more than 100 types of quasicrystals were found, and quasicrystals were recognized as the third class of solid states along with ordinary crystals and amorphous. However, the pace of the discovery has slowed significantly in recent years.
A joint research group of the Institute of Statistical Mathematics, the University of Tokyo, and Tokyo University of Science has demonstrated that machine learning algorithms can be used to learn the compositional patterns of quasicrystals found so far and predict the chemical composition of new quasicrystals. Furthermore, by extracting the input- output rules inherent in the black box model of machine learning, they were able to uncover the laws of quasicrystal phase formation. These laws can be expressed in five simple equations. These may serve as design guidelines for material searches, which have been long sought in quasicrystal research.