Critical Temperature Prediction for a Superconductor: A Variational Bayesian Neural Network Approach

Abstract: Much research in recent years has focused on using empirical machine learning approaches to extract useful insights on the structure-property relationships of superconductor material. Notably, these approaches are bringing extreme benefits when superconductivity data often come from costly and arduously experimental work. However, this assessment cannot be based solely on an open black-box machine learning, which is not fully interpretable, because it can be counter-intuitive to understand why the model may give an appropriate response to a set of input data for superconductivity characteristic analyses, e.g., critical temperature. The purpose of this study is to describe and examine an alternative approach for predicting the superconducting transition temperature $T_c$ from SuperCon database obtained by Japan's National Institute for Materials Science. We address a generative machine-learning framework called Variational Bayesian Neural Network using superconductors chemical elements and formula to predict $T_c$. In such a context, the importance of the paper in focus is twofold. First, to improve the interpretability, we adopt a variational inference to approximate the distribution in latent parameter space for the generative model. It statistically captures the mutual correlation of superconductor compounds and; then, gives the estimation for the $T_c$. Second, a stochastic optimization algorithm, which embraces a statistical inference named Monte Carlo sampler, is utilized to optimally approximate the proposed inference model, ultimately determine and evaluate the predictive performance.