Supervised Deep Learning Prediction Of The Formation Enthalpy Of Complex Phases Using A Dft Database: The Sigma-Phase As An Example

Machine learning (ML) methods are becoming the state-of-the-art in numerous domains, including material sciences. In this manuscript, we demonstrate how ML can be used to efficiently predict several properties in solid-state chemistry applications, in particular, to estimate the heat of formation of a given complex crystallographic phase (here, the sigma-phase, tP30, D8(b)). Based on an independent and unprecedented large first principles dataset containing about 10,000 sigma-compounds with n = 14 different elements, we used a supervised learning approach to predict all the similar to 500,000 possible configurations. From a random set of similar to 1000 samples, predictions are given within a mean absolute error of 23 meV at(-1) (similar to 2 kJ mol(-1)) on the heat of formation and similar to 0.06 angstrom on the tetragonal cell parameters. We show that deep neural network regression results in a significant improvement in the accuracy of the predicted output compared to traditional regression techniques. We also integrated descriptors having physical nature (atomic radius, number of valence electrons), and we observe that they improve the model precision. We conclude from our numerical experiments that the learning database composed of the binary-compositions only, plays a major role in predicting the higher degree system configurations. Our results open a broad avenue to efficient high-throughput investigations of the combinatorial binary computations for multicomponent complex intermetallic phase prediction.