These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generator...

Abstract Cluster expansion (CE) has gained an increasing level of popularity in recent years, and its applications go far beyond original root binary alloys, reaching even complex crystalline systems often used energy materials research. Similar to other modern machine learning approaches science, many strategies have been proposed for training fitting the CE models first-principles calculation...