The formation energy (Hf) is one of the important properties associated with the thermodynamic stability of ABO3-type perovskite. In this work, two-stage machine learning based on hierarchical ...clustering and regression was designed for improving the prediction values of the density-functional theory (DFT) Hf of ABO3-type perovskites. A global dataset was clustered into Cluster 1 and Cluster 2 using the CHI (the Calinski-Harabasz index). To compare the prediction performances of Hf, DTR (decision tree regression), GBRT (gradient boosted regression trees), RFR (random forest regression) and ETR (extra tree regression) were applied to build models of Cluster 1, Cluster 2 and the global dataset, respectively. The results showed that all four different regression models of Cluster 1 had a higher R2, and lower MSE and MAE than those of the global dataset, while the models of Cluster 2 were poorer. Meanwhile, the GBRT model of Cluster 1 achieved a higher R2 of 0.917, and lower MSE and MAE of 0.033 eV/atom and 0.125 eV/atom. We further validated and compared the generalization ability of the models by predicting the Hf of ABO3-type perovskite previously unseen in the training set. The two-stage machine-learning models proposed here can provide useful guidance for accelerating the exploration of materials with desired properties.
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