Deep Learning of Superconductors I: Estimation of Critical Temperature of Superconductors Toward the Search for New Materials

High-temperature superconductors have a lot of promising applications: quantum computers, high-performance classical computers, green energy, safe and high-speed transportation system, medical appliance, and etc. However, to discover new superconductors is very difficult. It is said that only $3\%$ of candidate materials become superconductors. We do not have satisfactory theory of high-temperature superconductors yet, and computational methods do not work either. On the other hand, the data has accumulated. Deep learning suits the situation. We introduce following two methods into deep learning: (1) in order to better represent material information and make good use of our scientific knowledge into deep learning, we introduce the input data form representing "material as image from periodic table with four channels corresponding to s, p, d, and f of electron orbit", (2) we introduce the method, named "garbage-in", to make use of the non-annotated data, which means the data of materials without any critical temperature $T_c$ in this case. We show that the critical temperature is well predicted by deep learning. In order to test the ability of the deep neural network it is good if we have the list of materials, which it is hard to tell whether they become superconductors or not from human expert in advance. We use the list made by Hosono's group as such. The test is to predict if a material becomes superconductor beyond $10$ Kelvin or not, and the neural network is trained by the data before the list was made. The neural network achieved accuracy $94\%$, precision $74\%$, recall $62\%$, and f1 score $67\%$. Compared to the baseline precision $9\%$, which is obtained from a positive prediction to randomly selected material, our deep learning has very good precision. We make a list of candidate materials of superconductors, and we are preparing for the experiments now.