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Physics-based, atom-centered machine learning (ML) representations have been instrumental to the effective integration of ML within the atomistic simulation community. Many of these representations build off the idea of atoms as having spherical, or isotropic, interactions. In many communities, there is often a need to represent groups of atoms, either to increase the computational efficiency of simulation via coarse-graining or to understand molecular influences on system behavior. In such cases, atom-centered representations will have limited utility, as groups of atoms may not be well-approximated as spheres. In this work, we extend the popular Smooth Overlap of Atomic Positions (SOAP) ML representation for systems consisting of non-spherical anisotropic particles or clusters of atoms. We show the power of this anisotropic extension of SOAP, which we deem AniSOAP, in accurately characterizing liquid crystal systems and predicting the energetics of Gay–Berne ellipsoids and coarse-grained benzene crystals. With our study of these prototypical anisotropic systems, we derive fundamental insights on how molecular shape influences mesoscale behavior and explain how to reincorporate important atom–atom interactions typically not captured by coarse-grained models. Moving forward, we propose AniSOAP as a flexible, unified framework for coarse-graining in complex, multiscale simulation. 

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.