Persistent Homology and Materials Informatics
Mickaël Buchet, Yasuaki Hiraoka, Ippei Obayashi · 2018
This paper provides an introduction to persistent homology and a survey of its applications to materials science. Mathematical prerequisites are limited to elementary linear algebra. Important concepts in topological data analysis such as persistent homology and persistence diagram are explained in a self-contained manner with several examples. These tools are applied to glass structural analysis, crystallization of granular systems, and craze formation of polymers.