Predefined attention-focused mechanism using center-environment features: a machine learning study of alloying effects on the stability of Nb5Si3 alloys†

Digital encoding of material structures using graph-based features combined with deep neural networks often lacks local specificity. Additionally, incorporating a self-attention mechanism increases architectural complexity and demands extensive data. To overcome these challenges, we developed a Center-Environment (CE) feature representation—a less data-intensive, physics-informed predefined attention mechanism. The pre-attention mechanism underlying the CE model shifts attention from complex black-box machine learning (ML) algorithms to explicit feature models with physical meaning, reducing data requirements while enhancing the transparency and interpretability of ML models. This CE-based ML approach was employed to investigate the alloying effects on the structural stability of Nb₅Si₃, guiding data-driven compositional design for ultra-high-temperature NbSi superalloys. The CE features leveraged the Atomic Environment Type (AET) method to characterize the local low-symmetry physical environments of atoms. The optimized CE_AET models reasonably predicted double-site substitution energies in α-Nb₅Si₃, achieving a mean absolute error (MAE) of 329.43 meV per cell. The robust transferability of the CE_AET models was demonstrated by their successful prediction of untrained β-Nb₅Si₃ structures. Site occupancy preferences were identified for B, Si, and Al at Si sites and for Ti, Hf, and Zr at Nb sites within β-Nb₅Si₃. This CE-based ML approach represents a broadly applicable and intelligent computational design method capable of handling complex crystal structures with strong transferability, even when working with small datasets.