An Explainable AI for Magnetic Function Analysis : Extended Free Energy Model

Abstract

Microscopic image plays a crucial information in functional design, particularly in data-driven materials science. However, extracting meaningful insights from imaging data remains a challenge. This study proposes the Extended Landau Free Energy Model, which integrates persistent homology and machine learning to quantitatively analyze magnetization reversal and pinning mechanisms in nanoscale materials. Using persistent homology, we extract topological features from domain structures and apply principal component analysis (PCA) to construct an energy landscape that describes magnetization reversal dynamics. Ridge regression is employed to correlate extracted features with magnetostatic and exchange energies, enabling a decomposition of energy barriers into their respective interactions. Our results clarify the pinning mechanism by quantifying the contributions of static and exchange interactions, and visualizing their spatial distribution via Hadamard product-based analysis. This method provides a detailed representation of pinning and depinning processes, revealing how structural heterogeneities influence energy barriers. Beyond magnetism, this framework offers broad applications in nanotechnology and data-driven materials science.