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Page 10 of 19 Tang et al. J. Mater. Inf. 2025, 5, 38 https://dx.doi.org/10.20517/jmi.2025.05

Table 2. ML prediction results of substitution energies (eV/cell) for Nb and α-Nb Si alloys using SVR and RF methods
5
3
RMSE (SVR) RMSE (RF)
Data sets (No. of data points)
Training Test Hyperparameter l training test
Nb (210) 0.077 0.092 0.1 0.170 0.248
Nb -Nb Si (588) 0.195 0.264 0.1 0.316 0.476
I 5 3
Nb -Nb Si (1,764) 0.189 0.271 0.5 0.361 0.514
3
II
5
Si -Nb Si (784) 0.227 0.269 0.1 0.252 0.347
I 5 3
Si -Nb Si (392) 0.047 0.115 0.1 0.254 0.359
3
5
II
Combined Nb Si (3,528) 0.416 0.495 0.5 0.675 0.780
5 3
ML: Machine learning; SVR: support vector regression; RF: random forest; RMSE: root mean square error.

Figure 5. Correlation plots between ML model-predicted and DFT reference (“exact”) values of substitution energies (in eV/cell) of
alloy systems for different datasets. (A) Nb alloys, (B) Nb -Nb Si alloys, (C) Nb -Nb Si alloys, (D) Si -Nb Si alloys, (E) Si -Nb Si 3
I
3
II
5
5
3
5
5
I
3
II
alloys, (F) combined data set. Blue points are for the training and red points for the test set. Correlation coefficients are given on the
plots (mean over 100 train-test splits). ML: Machine learning; DFT: density functional theory.