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We present a symmetry-based systematic approach to explore the structural and compositional richness of two-dimensional materials. We use a ‘combinatorial engine’ that constructs candidate compounds by occupying all possible Wyckoff positions for a certain space group with combinations of chemical elements. These combinations are restricted by imposing charge neutrality and the Pauling test for electronegativities. The structures are then pre-optimized with a specially crafted universal neural-network force-field, before a final step of geometry optimization using density-functional theory is performed. In this way we unveil an unprecedented variety of two-dimensional materials, covering the whole periodic table in more than 30 different stoichiometries of form A_nB_mor A_nB_mC_k. Among the discovered structures, we find examples that can be built by decorating nearly all Platonic and Archimedean tessellations as well as their dual Laves or Catalan tilings. We also obtain a rich, and unexpected, polymorphism for some specific compounds. We further accelerate the exploration of the chemical space of two-dimensional materials by employing machine-learning-accelerated prototype search, based on the structural types discovered in the systematic search. In total, we obtain around 6500 compounds, not present in previous available databases of 2D materials, with a distance to the convex hull of thermodynamic stability smaller than 250 meV/atom.

 

Abstract In recent years, we have been witnessing a paradigm shift in computational materials science. In fact, traditional methods, mostly developed in the second half of the XXth century, are being complemented, extended, and sometimes even completely replaced by faster, simpler, and often more accurate approaches. The new approaches, that we collectively label by machine learning, have their origins in the fields of informatics and artificial intelligence, but are making rapid inroads in all other branches of science. With this in mind, this Roadmap article, consisting of multiple contributions from experts across the field, discusses the use of machine learning in materials science, and share perspectives on current and future challenges in problems as diverse as the prediction of materials properties, the construction of force-fields, the development of exchange correlation functionals for density-functional theory, the solution of the many-body problem, and more. In spite of the already numerous and exciting success stories, we are just at the beginning of a long path that will reshape materials science for the many challenges of the XXIth century.