Topological data analysis of domain pattern formation in materials

Topological data analysis is a data analysis method that focuses on the topological structure of data, and extracts topological features such as holes and network structures from the data with structures. A feature value called persistent homology is prepared for topological data analysis. In the persistent homology introduced in this paper, it is possible to appropriately extract physically useful information by adding spatial scale information. First, this paper closes the eyes on the mathematical rigor and tries to explain the persistent homology group by referring to the formation process of the ferromagnetic magnetic domain structure using the time dependent Ginzburg-Landau equation. Then, it describes the reason why the analysis using the persistent homology group is useful for the analysis of material structures. It was found that in the non-linear and non-equilibrium pattern formation process, the persistence diagram can capture the behavior best. This suggests that the feature value extraction based on the persistent homology group is effective as a feature value space for understanding and modeling the pattern formation process that forms an aperiodically ordered structure. (A.O.)