Machine Learning-Aided High-Throughput First-Principles Calculations to Predict the Formation Energy of μ Phase

The mu phase is a type of hard and brittle constituent that exists in high-temperature alloys. The formation energy is a crucial thermochemical datum, and the accurate calculation of the formation energy of the mu phase contributes to the material design of high-temperature alloys. Traditional first-principles calculations demand significant computational time and resources. In this study, an innovative machine learning (ML)-based approach to accurately predict the formation energy of the mu phase is proposed. This approach involves the utilization of six algorithms and two model evaluation methods to construct the ML models. Leveraging a comprehensive data set containing 1036 binary configurations of the mu phase, the model trained using a 10-fold cross-validation technique, and the multilayer perceptron (MLP) algorithm achieves a mean absolute error (MAE) of 23.906 meV/atom. To validate its generalization performance, the trained model is further validated on 900 ternary configurations, resulting in an MAE of 32.754 meV/atom. Compared with solely using traditional first-principles calculations, our approach significantly reduces the computational time by at least 52%. Moreover, the ML model exhibits exceptional accuracy in predicting the lattice parameters of the mu phase. The MAE values for the a and c parameters are 0.024 and 0.214 angstrom, respectively, corresponding to low error rates of only 0.479 and 0.578%. Additionally, the ML model was utilized to accurately predict the formation energy of all of the possible ternary configurations. To enhance accessibility to the formation energy data of the mu phase, a user-friendly graphical user interface (GUI) was developed, ensuring convenient usability for researchers and practitioners.