Machine Learning Prediction of Vacancy Formation Energies in CoNiCrFe High-Entropy Alloy: The Role of Atomic Descriptors and Local Chemical Order

Vacancy formation energy governs atomic transport, radiation defect evolution, and phase stability in high-entropy alloys (HEAs). To develop an efficient predictive framework for this critical property, we employ support vector regression (SVR) to model vacancy formation energies in both random solid solution (RSS) and locally chemically ordered (LCO) structures. Three classes of atomic descriptors─neighbor-specific descriptors, average structural metrics, and smooth overlap of atomic positions (SOAP)─were used to capture the complexity of local environments. Among these, SOAP, which capture many-body correlations and provides rotationally and translationally invariant fingerprints, consistently achieved the highest accuracy, with test R² values of up to ∼0.89 for RSS and ∼0.96 for LCO. The enhanced predictability of LCO-based models results from compositional inhomogeneity, where regions such as Cr-rich clusters strengthen composition-energy correlations that simplify the learning task. While models trained on the more diverse RSS vacancy formation energies generalized better to LCO environments, a mixed training set containing RSS and LCO dataset was shown to maintain high performance on diverse atomic environments. These findings demonstrate that descriptor choice and structural representation are critical for machine learning predictability of defect energetics and provide a framework that can be extended to other defect properties in complex alloys.