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

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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> . 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> . 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. As a result, in comparison with the standard evaluation metrics, the results are promising and also agree with the existing models prevalent in the field. The R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> value obtained is very close to the best model (0.94), whereas a considerable improvement is seen in the RMSE value (3.83 K). Notably, the proposed model is known as the first of its kind for predicting a superconductor's T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> .

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