Physically explainable statistical learning of flat bands in stoichiometric materials from the periodic table

Flat-band materials (FBMs) serve as a platform for a variety of exotic properties and applications, such as strongly correlated states, topological states, and superconductivity. However, reported FBMs highly rely on materials engineering, such as Moir\'e lattices. Here, we demonstrate the acceleration of intrinsic FBM discovery using explainable statistical learning within a periodic table representation (PTR). Our model achieves validation accuracies of 0.81--0.97 for ${X}_{2}YZ$ full-Heusler alloys across three different databases and 0.84 for $\mathrm{AB}{\mathrm{C}}_{3}$ perovskites. Our interpretable model and statistical analysis reveal several important valence electron-related features for FBMs, supported by atomic orbital hybridization theory. We further discuss various physical properties and applications strongly associated with flat bands, including topology, thermal conductivity, electron-phonon coupling, and superconductivity. Finally, we predict 25 high-potential, previously unreported flat-band Heusler alloys using the PTR model, validated by first-principles calculations.