New model uses persistent homology to analyze topological features in data and extract inhomogeneous structural features from the domain images. Entropy-extended free energy landscape reveals magnetization reversal in maze domains. The explainable entropy-feature-eXtended Ginzburg-Landau (eX-GL) model maps complex maze-like magnetic domain structures into a free energy landscape, enabling identification of key energy barriers and mechanisms driving temperature-dependent magnetization reversal.