Explainable analysis of the complex maze magnetic domain structure through extension of the Landau free energy model by adding an entropy feature

Maze magnetic domains exhibit complex, temperature-dependent behavior that impacts energy loss in soft magnets, yet their magnetization reversal mechanisms remain poorly understood due to current model limitations. To address this gap, we develop an entropy-extended Landau free energy model that incorporates thermal effects into the analysis of magnetic domain. We employ a data-driven pipeline combining persistent homology, energy decomposition, and principal component analysis to construct an interpretable model that quantifies structure-property relationships and enables causal analysis of magnetic pattern formation. Using this approach, we trace entropy increases to their origins in initial domain configurations and quantify energy transfer among entropic, demagnetization, and exchange contributions. We also find that domain wall lengthening tracks increasing structural complexity, yielding previously inaccessible insights into magnetization reversal mechanism and enabling automated visualization. Our entropy-augmented model provides an explainable framework to decipher magnetization processes and guide the design of magnetic materials to reduce energy loss.