Interpretable formation-energy structure from composition, density, and band-gap descriptors

Abstract Thermodynamic constraints strongly shape which inorganic crystals can form and persist, yet exhaustive first-principles exploration of multicomponent inorganic materials space remains computationally prohibitive. Here we examine how formation energy per atom relative to elemental reference states ( $$\:{E}_{f}$$ ) is organised across inorganic crystals using a compact descriptor-level machine-learning audit. We construct a controlled exploratory subset of 5000 Materials Project compounds and train a Random Forest regressor using compact descriptors derived from formula-based composition statistics, together with two DFT-derived indicators, mass density ( $$\:\rho\:$$ ) and electronic band gap ( $$\:{E}_{g}$$ ). Because density and band gap are DFT-derived quantities in the Materials Project dataset, the final model is interpreted as a DFT-assisted analysis of descriptor information content. The compact descriptor model achieves MAE = 0.188 eV/atom, RMSE = 0.407 eV/atom and $$\:{R}^{2}=0.871$$ on the independent 1000-compound IID test set. Ablation analyses quantify the incremental predictive contribution of $$\:\rho\:$$ and $$\:{E}_{g}$$ beyond a strictly formula-derived compact baseline, which already captures substantial formation-energy signal (MAE = 0.223 eV/atom, $$\:{R}^{2}=0.822$$ ). Additional tabular baselines using the same compact descriptors, including ExtraTrees, LightGBM, XGBoost and CatBoost, give broadly comparable performance, confirming that the main conclusions are not specific to a single Random Forest implementation. To probe robustness and generalisation limits, we perform learning-curve analysis, compositionally stringent leave-one-element-out tests, and an automatic rare-element out-of-distribution split. Learning curves show systematic improvement with training size and partial flattening beyond approximately 2000–3000 training compounds. Prediction spread is used as a non-calibrated operational risk indicator, with higher spread associated with larger absolute errors under both IID and rare-element OOD conditions. Low-dimensional PCA/UMAP embeddings are retained as qualitative descriptor-space visual diagnostics of the sampled representation. The results show that substantial formation-energy structure can be recovered from physically interpretable and auditable descriptors while explicitly identifying the limits imposed by distribution shift, exploratory dataset scale, and the DFT-derived nature of structural/electronic inputs.