We first evaluated the accuracy of both CML and GNN models for predicting E f by calculating the R 2 scores and MAE values on the test sets of three datasets, including MP, OQMD, and CMR (see Table ). Other metrics to assess the model performance, including RMSE and MSE can be found in Tables . As shown in Table , all the models exhibit impressive accuracy in predicting E f across all three databases with R 2 exceeding 0.9 (Figures ). In particular, all models adopt higher R 2 values in the OQMD dataset than in MP and CMR. Furthermore, for any given dataset, GNN based models demonstrate superior accuracy compared to CML models, as evidenced by the higher R 2 of about 0.99 and lower MAE values. Among the four GNN-based models, Matformer consistently achieves the highest prediction accuracy among all the datasets.