Unsupervised topological learning for atomic structures identification

We propose an unsupervised learning methodology build on a Gaussian mixture model computed on topological descriptors from persistent homology, for the structural analysis of materials at the atomic scale. Based only on atomic positions and without textit{a priori} knowledge, our method automatically identifies relevant local atomic structures in a system of interest. Along with a complete description of the procedure, we provide a concrete example of application by analysing large-scale molecular dynamics simulations of bulks crystal and liquid as well as homogeneous nucleation events of elemental Zr at the nose of the time-temperature-transformation curve. This method opens the way to deeper and autonomous studies of structural dependent phenomena occurring at the atomic scale in materials.