Abstract The disordered nature of amorphous materials like metallic glasses has long hindered the establishment of well-defined structure-property relationships. Although it is widely recognized that short-range orders (SROs) within the first nearest-neighbor shell do not sufficiently characterize these materials, identifying the optimal characteristic length scale for capturing richer structural information remains elusive. Here, we resolve this ambiguity using a dual machine learning (ML) approach, which identifies the Radius of Informative Structural Environments (RISE) in a prototypical Zr-Cu metallic glass system. A top-down, reductionist approach, integrating SOAP descriptor with XGBoost model, demonstrates that the atomic environments within 5 Å radius entail maximal structural diversity and information density, leading to the optimal performance of the model on predicting given samples’ configurational energies. Concurrently, a bottom-up, emergentist Vision Transformer (ViT) architecture, designed to autonomously learn structural patterns from voxelized atomic configurations, shows that its predictive performance saturates when the effective communication length between its input patches reaches an equivalent spherical radius of ~5 Å. The striking convergence of these independent ML strategies provides compelling, data-driven evidence for the existence of an intrinsic, structurally informative length scale in metallic glasses. Additional robustness checks across multiple glassy materials with various elements numbers and bonding types confirm such RISE is not an artifact of encoding parameters or system size and aligns with existing experimental and computational insights.
Wang et al. (2026) studied this question.