An Interpretable and Transferable Physics-Aware Machine-Learning Framework for Stability Prediction of Dual-Atom Alloys

Abstract

Dual-atom alloys (DAAs) embedded in metallic surfaces constitute an emerging catalytic platform fundamentally distinct from the widely studied carbon-supported dual-atom sites, as they enable intrinsic metal–metal cooperation within an active metallic environment. However, a systematic understanding of their structure–stability relationships remains elusive, mainly due to the prohibitive cost of exploring the vast space of compositions, crystal surfaces, and atomic configurations. Here, using Cu-based DAAs as a prototypical platform, we construct a library of 6804 candidate structures spanning nine crystal planes and two representative dual-atom configurations. Density functional theory (DFT)-calculated formation energies for 930 representative structures (13.7% of the library) are employed to train a physics-informed residual multilayer perceptron model combined with 5-fold ensemble learning. The model achieves high predictive accuracy with cross-validation R2 > 0.906 and demonstrates robust transferability across different crystal planes and structural motifs, outperforming conventional machine-learning baselines. Interpretable SHAP analysis indicates that electronic structure descriptors predominantly govern stability, with geometric compatibility contributing as a secondary factor. Systematic stability trends are identified, including a thermodynamic preference for diagonal configurations on the (100), (311), and (411) surfaces, linear-close configurations on the (110), (111), and (211) surfaces, and enhanced stability for noble-metal dopants, such as Au, Pt, and Pd. Electronic structure analysis further establishes a clear correlation between formation energy and the dopant d-band center, with greater stability achieved when the d-band center is located farther from the Fermi level. With the training on a limited number of DFT-calculated samples, this physics-aware and transferable machine-learning framework enables rapid and data-efficient prediction of dual-atom alloy stability. The approach is readily extensible to diverse crystal surfaces and alloy systems, providing a generalizable theoretical foundation for the thermodynamic screening and rational design of DAAs with high synthetic feasibility in energy catalysis.