Permutation invariant neural network prediction of vacancy formation under deformation and varying chemical environment in FCC high entropy alloys
Vacancy formation energies govern diffusion, irradiation damage, phase stability, and dynamic failure in high-entropy alloys (HEAs), yet their strong dependence on local chemical environments and mechanical deformation makes atomistic calculations prohibitively expensive for large-scale studies. Here, we develop an atomistically informed permutation invariant machine learning framework for predicting strain dependent vacancy formation energies in FCC HEAs from local atomic environments. The model employs a vacancy-centered representation constructed from objective geometric descriptors together with invariants of the local deformation gradient, enabling the coupled effects of chemical disorder and finite deformation to be learned within a unified framework. Atomistic simulations reveal that volumetric deformation is the dominant factor controlling the average variation in vacancy formation energy, whereas shear deformation has a comparatively minor influence. At the same time, substantial site to site variability persists under identical macroscopic loading, demonstrating that local chemical environments govern the statistical distribution of vacancy energetics beyond species-averaged trends. The proposed framework accurately predicts vacancy formation energies across diverse deformation states while providing orders-of-magnitude faster evaluation than direct atomistic simulations. These results establish an efficient route for incorporating stress-dependent defect energetics into multiscale models of diffusion, irradiation damage, and dynamic failure in chemically complex alloys.