Predicting vacancy formation energies in refractory non-dilute random alloys using improved graph-based machine learning models trained on density functional theory data

This study employs four machine learning (ML) models—random forest (RF), XGBoost, graph convolutional networks (GCN), and graph attention networks (GAT)—to predict vacancy formation energies (VFEs) in refractory non-dilute random alloys including pure metals, binary, ternary, quaternary, and quinary systems based on Mo, Nb, Ta, V, and W. Training data are generated from density functional theory calculations. Among all elements, W has the highest VFE on average (2.866 → 3.517 eV from pure metal to ternary), while Ta is the only element whose VFE rises monotonically (2.841 → 3.262 eV from pure metal to quinary). In tree-based tabular models (RF, XGBoost), each chemical composition is encoded as a five-dimensional vector of elemental fractions on the Mo–Nb–Ta–V–W basis, augmented with a categorical indicator of the specific element in a certain alloy for which the vacancy is created, and features are standardized to balance input scales during training. In graph models (GCN, GAT), each composition is represented as a small graph whose nodes carry per-element descriptors (fraction, atomic number, and Magpie features), while edges summarize simple pairwise chemistry (such as fraction interactions and differences in atomic number, electronegativity, covalent radius, and Mendeleev number). All four models achieve high accuracy in predicting VFEs across alloy orders, with graph-based approaches capturing chemistry-aware trends beyond fixed tabular descriptors. Among the four, GCN attains the highest accuracy with R2=0.972, root mean squared error =0.051 eV, and mean absolute error =0.042 eV, outperforming GAT and the tabular baselines. These results underscore the promise of graph-based ML for rapid, reliable prediction of VFEs in the refractory alloy design.