Procedure to Reveal the Mechanism of Pattern Formation Process by Topological Data Analysis

TL;DR

This paper introduces an analytical procedure combining topological data analysis and machine learning to interpret pattern formation processes, exemplified by magnetic domain patterns, and proposes a reduction model for understanding their dynamics.

Contribution

It develops a novel method to interpret TDA features in physical phenomena and applies it to magnetic domain pattern formation, offering insights into underlying dynamics.

Findings

Quantified non-trivial domain pattern classifications

Revealed the nature of magnetic domain dynamics

Proposed a candidate reduction model

Abstract

Topological data analysis (TDA) is a versatile tool that can be used to extract scientific knowledge from complex pattern formation processes. However, the physics correspondence between the features obtained from TDA and pattern dynamics does not agree one-to-one, and the physical interpretation of the TDA features needs to be set appropriately according to the phenomenon to be analyzed. In this study, we propose an analytical procedure to physically interpret pattern dynamics through TDA and machine learning techniques. The proposed procedure was applied to the process of magnetic domain pattern formation to quantify non-trivial domain pattern classifications and reveal the nature of the underlying dynamics. On the basis of these findings, we also propose a candidate reduction model to understand the nature of magnetic domain formation.