Machine learning aided high-throughput first-principles calculations to predict the formation enthalpy of σ phase

The σ phase is a topologically close-packed phase and can significantly influence the performance and properties of materials. Accurate prediction the formation enthalpy of the σ phase is crucial for the development of high-performance materials. First-principles calculations based on density functional theory (DFT) have been employed to study the formation enthalpy of the σ phase, but this approach requires a amount of computational resources and time. In this study, we propose a machine learning (ML) method to predict the formation enthalpy of the σ phase. This method employs a first-principles dataset containing 1342 configurations of the binary σ phases for model training and testing. Among the algorithms used, the Multi-Layer Perceptron algorithm demonstrated the highest predictive accuracy, with the mean absolute error (MAE) of 22.881 meV/atom, which is comparable to the existing ML prediction model based on first-principles calculations. The trained model was then utilized to predict the formation enthalpy of the 1177 untrained ternary configurations, achieving a significant reduction in computational time of over 59% compared to traditional first-principles calculations. Furthermore, the model was validated for lattice parameters prediction, achieving the MAE of 0.073 Å and 0.048 Å for the a and c, respectively. A Graphical User Interface (GUI) was developed. Finally, we predicted the formation enthalpy of all the possible ternary configurations, which is comparable to the MAE of DFT-calculations itself.