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

The μ 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 μ 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 μ 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 μ 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 μ phase. The MAE values for the a and c parameters are 0.024 and 0.214 Å, 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 μ phase, a user-friendly graphical user interface (GUI) was developed, ensuring convenient usability for researchers and practitioners.