# Computational Screening of New Perovskite Materials Using Transfer Learning and Deep Learning
## 3 Results and Discussions
### Screening Results Analysis  
Our CNN model is able to make robust, fast predictions, so it can be used to screen 21,316 materials to discover new and stable perovskite materials. After screening by the M2 model, of 21,316 hypothetical ABO\({}_{3}\) materials, 4147 had formation energy less than 0. More specifically, 5106 were ABBr\({}_{3}\), 5236 were ABCl\({}_{3}\), and 4279 were ABI\({}_{3}\). The specific formation energy prediction value range distribution is shown in Figure 8. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **RMSE** & **MAE** & **R\({}^{2}\)** \\ \hline ElemNet & 0.49 & 0.64 & 0.52 \\ RF & 0.36 & 0.27 & 0.83 \\ GBR & 0.35 & 0.25 & 0.84 \\ CNN & 0.34 & 0.24 & 0.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: RMSE (_eV/atom_), MAE (_eV/atom_), and R\({}^{2}\) values of cross-validation results of all prediction models using the Magpie descriptor. CNN, convolutional neural network. Figure 7: Prediction performance comparison of transfer learning model and the baseline model, both using Magpie descriptors. Left: transfer learning model trained with 578 samples labeled by M1 model +570 samples with density functional theory (DFT) formation energies. Right: baseline model trained only with 570 samples with DFT formation energies. Figure 8: _Cont._  
The candidate materials screened out are not necessarily perovskite materials, even though the formation energy may be less than zero. Here we use the new tolerance coefficient \(\tau\) as discussed before to further screen the selected candidate materials. If the \(\tau\) of a candidate material is calculated to be less than 4.18, the candidate material has a high probability of being a stable perovskite material. Since \(\tau\) requires that the ionic radius of the A cation is greater than the ionic radius of the B cation, a portion of the candidate material is therefore filtered out. After screening the new tolerance coefficient \(\tau\), there are 625 ABO\({}_{3}\) with \(\tau\) less than 4.18 along with 52 ABBr\({}_{3}\), 55 ABCl\({}_{3}\), and 32 ABI\({}_{3}\). By reviewing the literature, we found that 98 of the 626 ABO\({}_{3}\)s were reported in [27], and 98 perovskites were proved to be stable by DFT calculations. In addition, it was reported [41] that the doped lanthanide BaSnO\({}_{3}\) can be used as the material of the electron transfer layer for a highly efficient and stable solar cell. This material showed up in our screening results. The specific 98 ABO3s are shown in Table 5. In addition to these 98 compounds, literature [42] proved that one of our predictions, SrMoO\({}_{3}\) in 625 ABO\({}_{3}\), has paramagnetism. Among the 32 ABI\({}_{3}\) screened out by our model, literature [43] verified that CsPbI\({}_{3}\) can be surface-coated with surfactants and environmental conditions are stable. It is expected to be used for light collection or LEDs. Among the 52 ABCl\({}_{3}\) screened out, literature [44] calculated CsPbCl\({}_{3}\) by DFT, and found that the reduction of band gap is due to the limiting effect of carriers, and the increasing number of perovskite layers. Among the 55 ABBr\({}_{3}\) screened out, [PERSON] et al. [45] for the first time reported the temperature dependence of the spontaneous emission (ASE) characteristics of CsPbBr\({}_{3}\) nanocrystalline thin films. [PERSON] et al. [46] verified the luminescence of colloidal CsPbBr\({}_{3}\) perovskite nanocrystals, which surpass traditional quantum dots.