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Page 4 of 20 Zhu et al. J. Mater. Inf. 2025, 5, 8 https://dx.doi.org/10.20517/jmi.2024.76

record the space group, unit cell parameters, atomic coordinates, and atom types of crystalline materials.
After data collection, the raw data is cleaned and preprocessed to ensure data quality and enhance the
model’s predictive performance. Incomplete or outlier data points are excluded, such as those without
density or crystal structure values. A total of 7,253 binary intermetallic compound density data are gathered.
These compounds cover seven major crystal structure types: cubic, hexagonal, monoclinic, orthorhombic,
trigonal, tetragonal, and triclinic. The diversity of these structural types better represents the complexity of
intermetallic compounds in practical applications, providing comprehensive training data for subsequent
machine learning modeling.

The pie chart in Figure 1A shows the proportion of data for each crystal structure. Cubic and hexagonal
structures are the most common, comprising 29% and 28.3% of the data, respectively. The triclinic structure
has the fewest data points, representing only 0.5%. In addition, the periodic table in Figure 1A shows the
frequency of elements in the intermetallic compound density dataset. The higher the frequency, the darker
the corresponding color. The violin plot illustrates the density distributions of compounds across six crystal
structures, as shown in Figure 1B. Each structure is represented by a distinct violin plot. The shape and
width of each plot reflect the density distribution, and the white dots within the plots indicate the median
density for each crystal structure.

Dataset splitting and feature construction
The dataset in this study is split using the 80/20 method, with 80% of the data used for the training set and
the remaining 20% for the test set. Moreover, to further assess the model’s generalization capability and
prediction accuracy on complex compounds, density data from 237 ternary and 33 quaternary intermetallic
compounds are collected as an independent test set. These multicomponent compound samples cover
various element combinations and complex crystal structures, enabling a more comprehensive evaluation of
the model’s performance. This study employs several common evaluation metrics to comprehensively
evaluate the model’s performance. These include regression metrics such as root mean square error
(RMSE) , mean absolute error (MAE) , and the coefficient of determination (R ) , as well as
[30]
[29]
2 [31]
classification metrics such as precision, recall, F1-score, and receiver operating characteristic (ROC)
curves .
[32]
The Python library XenonPy is leveraged to introduce 58 properties of 94 elements (H to Pu), covering
multiple aspects such as electronic structures, physicochemical properties, and microscopic geometric
structures . An additional nine features related to bond energy are included, resulting in a total of 67
[33]
elemental features for constructing machine learning features and serving as input parameters for IGNN
model nodes. Detailed information on the 67 element features is given in Table 1. The min-max scaling
method is used to normalize the feature set, mapping all values between 0 and 1 to eliminate the influence of
scale differences on model performance . This process reduces the model’s sensitivity to specific numerical
[34]
ranges, preventing adverse effects on model training caused by large data ranges. Furthermore, it preserves
the relative distribution of the data while ensuring consistent learning efficiency across different features
during model training.

Machine learning algorithms and GNN model
In this study, various commonly used traditional machine learning models, along with the constructed
GNN model, are used to predict the density of binary intermetallic compounds. The traditional machine
learning models included linear regression (LR), support vector machine (SVM), K-nearest neighbors
(KNN), random forest (RF), and EXtreme gradient boosting (XGBoost). LR is a fundamental regression
model that assumes a linear relationship between independent and dependent variables. Although its
structure is simple, it can still perform effectively when the data exhibits linear characteristics. SVM