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Tang et al. J. Mater. Inf. 2025, 5, 38 https://dx.doi.org/10.20517/jmi.2025.05 Page 5 of 19

Figure 1. (A) Nb supercell BCC structure containing non-equivalent substitutional models of X Nb0 Y Nb1 and X Nb0 Y Nb2 ; (B) α-Nb Si BCT
5
3
conventional cell containing four non-equivalent sites: Nb , Nb , Si , and Si . The M (subscripts I) and L (subscripts II) represent the
II
II
I
I
more and less closely packed layers, respectively. BCC: Body-centered cubic; BCT: body-centered tetragonal.
where C and E refer to the center and environment atoms, respectively; i is the index for the elementary
property, and j denotes the index of the environment atoms. The variable p represents the i-th elementary
c,i
property of the center atom, while p denotes the i-th property of the j-th environment atom surrounding
E,j,i
the center atom. The weight ω reflects the influence of the elementary properties based on the distance r j
E,j
between the center and environment atoms. The weights are normally inversely proportional to the r j
distance.
It is well-known that feature engineering significantly influences the accuracy of ML modeling [2,3,30,42] . The
CE features are composite characteristics derived from an assembly of elementary property features,
incorporating local structural information as specified by the center and environment atoms
[Supplementary Text 1 and Supplementary Figure 1]. The CE features consist of two main types:

(1) Elementary property features: These are various physicochemical properties readily available from
fundamental databases , such as atomic mass, radius, electronegativity, and the number of valence
[43]
electrons, as well as properties of pure substances such as density, melting temperature, and bulk modulus.

(2) Compound property features: These features are constructed through a linear combination of the
elementary properties of the center or the environment atoms, with weights inversely proportional to the
distance between the center atom and the environment atom (r ).
-1
j
This approach allows CE features to effectively encode elementary properties along with local composition
and structure information, offering a comprehensive digital representation of the materials’ composition
and structure.