Unsupervised topological learning for identification of atomic structures

Abstract

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 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.

Dimensionality reduction of local structure in glassy binary mixtures

“…We have described the construction of several structural descriptors X(i) that characterize the first coordination shell of particle i, as given in Eq. ( 6), ( 9) and (19). Let the dimension of X(i) be M .…”

“…Unsupervised methods typically comprise two steps: (i) dimensionality reduction, to project the high-dimensional descriptor on a smaller subspace while retaining most of a) Electronic mail: dcoslovich@units.it the original information, and (ii) clustering, to identify groups of points in the dataset that share similar values of the (reduced) descriptor. This approach has been recently applied, for instance, to crystal structure identification in colloidal suspensions 17,18 and the study of partially ordered systems 16,19 . Recent studies have also tackled challenging problems of structural analysis in bulk disordered materials, such as simple models of supercooled liquids and glasses 20,21 , amorphous carbon 16,22 , and liquid water in normal and supercooled conditions 23,24 .…”

Roles of liquid structural ordering in glass transition, crystallization, and water's anomalies

“…Here we should note that identification of local structures, e.g., by using bond orientational order parameters [25] is not necessarily reliable, Recently, ma-chine learning has been used to detect the symmetry of a crystal structure more accurately, which may be helpful for a better description of crystal nucleation [159,160,161,162].…”