Fig. 3.

Evaluation of atom vectors of main-group elements on elpasolites ${\mathrm{A}\mathrm{B}\mathrm{C}}_2{\mathrm{D}}_6$ formation energy prediction. (A) Crystal structure of elpasolites ${\mathrm{A}\mathrm{B}\mathrm{C}}_2{\mathrm{D}}_6$. (B) Architecture of the one-hidden-layer neural network for formation energy prediction. Colored boxes represent atom vectors of atoms $A$, $B$, $C$, and $D$, respectively, and gray box in the hidden layer is representation of the elpasolites compound. (C) Trained weights on connections between the input layer and the hidden layer in the neural network for formation energy prediction using model-free atom vectors of dimension $d=10$. (D) Mean absolute test errors of formation energy prediction using different sets of atom features. Empirical features refer to the position of an atom in the periodic table, padded with random noise in expanded dimensions if necessary. Model-based features are atom vectors learned from our model-based method using an inverse-square score function (Materials and Methods). Model-free features are atom vectors learned from our model-free method. Error bars show the SDs of mean absolute prediction errors on five different random train/test/validation splits. (E) Comparison of exact formation energy and predicted formation energy using $d=20$ model-free atom vectors. Inset shows the distribution of prediction errors.