In terms of methods, this study is based on a dataset consisting of 280,569 compounds. The formation energies of these compounds were obtained through density functional theory (DFT) calculations. A system of 145 feature descriptors was constructed, covering stoichiometric properties, statistical properties of elements, electronic structure properties, and properties of ionic compounds, to comprehensively describe the characteristics of rare-earth compounds. Two ML models, random forest (RF) and neural network (NN), were selected to perform classification and regression tasks respectively. The 5-fold cross-validation was used to improve the reliability of the models. The min-max scaling technique was applied for data preprocessing, and an ensemble learning architecture was constructed to address the limitations of single model.

In the classification task, the RF and NN algorithms performed remarkably well. With 5-fold cross-validation, the accuracy reached approximately 0.97, and the F1 score was around 0.98, enabling the precise classification of compounds into stable or unstable categories. In the regression task, the mean absolute errors (MAE) of the formation energy predictions by the RF and NN models were 0.055 eV/atom and 0.071 eV/atom, respectively. This indicates that the model predictions are highly accurate and can, to a certain extent, replace complete DFT calculations. In the prediction analysis of systems outside the test set, six representative components were selected from the Materials Project database, covering binary, ternary, and quaternary systems. The prediction errors of all compositions were controlled within 0.5 eV/atom, and the error percentages were lower than 25%, demonstrating the strong extrapolation prediction ability of the models. When predicting the binary phase diagrams of rare-earth compounds La-Al and Ce-H using the trained models, the convex hull phase diagrams constructed through the ensemble learning architecture, which combines the prediction results of the RF and NN models, were highly consistent with those constructed from the Open Quantum Materials Database. The models successfully captured several metastable phases that were not present in multiple databases. Moreover, the convex hull distances of the predicted phases were mostly less than 0.1 eV/atom, with the maximum not exceeding 0.2 eV/atom.

In conclusion, this study successfully used ML models to predict the thermodynamic stability of rare-earth compounds. The constructed models demonstrated strong capabilities in classification and regression tasks. The ensemble learning architecture effectively improved the model performance, providing a promising tool for materials discovery in the field of rare-earth science and contributing to the research and development of new rare-earth compounds and the design of advanced materials.