Deep learning model for finding new superconductors

Exploration of new superconductors still relies on the experience and intuition of experts, and is largely a process of experimental trial and error. In one study, only 3% of the candidate materials showed superconductivity [Hosono et al., Sci. Technol. Adv. Mater. 16, (2015)]. Here, we report a deep learning model for finding new superconductors. We introduced the method named “reading periodic table” that represented the periodic table in a way that allows deep learning to learn to read the periodic table and to learn the law of elements for the purpose of discovering novel superconductors which are outside the training data. It is recognized that it is difficult for deep learning to predict something outside the training data. Although we used only the chemical composition of materials as information, we obtained an $R^2$ value of 0.92 for predicting $T_{\text{c}}$ for materials in a database of superconductors. We also introduced the method named “garbage-in” to create synthetic data of nonsuperconductors that do not exist. Nonsuperconductors are not reported, but the data must be required for deep learning to distinguish between superconductors and nonsuperconductors. We obtained three remarkable results. The deep learning can predict superconductivity for a material with a precision of 62%, which shows the usefulness of the model; it found the recently discovered superconductor ${\mathrm{CaBi}}_2$ and another one ${\mathrm{Hf}}_{0.5}{\mathrm{Nb}}_{0.2}{\mathrm{V}}_2{\mathrm{Zr}}_{0.3}$, neither of which is in the superconductor database; and it found Fe-based high-temperature superconductors (discovered in 2008) from the training data before 2008. These results open the way for the discovery of new high-temperature superconductor families. The candidate materials list, data, and method are openly available on the Internet.

Figure 1

Proposed method named reading the period table. (Top) The representation of a material by the method. The composition ratios of the material [26] are entered into the two-dimensional periodic table. We then divide the original table into four tables corresponding to s, p, d, and f blocks, which show the orbital characteristics of the valence electrons, to allow the deep learning model to learn the valence orbital blocks. The dimensions of the representation are $4\times 32\times 7$. The neural network learns the rules from the periodic table by convolutional layers. (Bottom) The representation by the method and neural network.

Figure 2

Scatter plot of predicted and true (SuperCon) $T_{\text{c}}$ values.

Figure 3

Histogram of the number of predicted FeSCs with $T_{\text{c}}>0\mathrm{K}$ (log scale).