Efficient Prediction of Quasi-Phase Equilibrium in KKS Phase Field Model via Grey Wolf-Optimized Neural Network

As the demand for advanced material design and performance prediction continues to grow, traditional phase-field models are increasingly challenged by limitations in computational efficiency and predictive accuracy, particularly when addressing high-dimensional and complex data in multicomponent systems. To overcome these challenges, this study proposes an innovative model, LSGWO-BP, which integrates an improved Grey Wolf Optimizer (GWO) with a backpropagation neural network (BP) to enhance the accuracy and efficiency of quasi-phase equilibrium predictions within the KKS phase-field framework. Three mapping enhancement strategies were investigated–Circle-Root, Tent-Cosine, and Logistic-Sine mappings–with the Logistic mapping further improved via Sine perturbation to boost global search capability and convergence speed in large-scale, complex data scenarios. Evaluation results demonstrate that the LSGWO-BP model significantly outperforms conventional machine learning approaches in predicting quasi-phase equilibrium, achieving a 14–28 reduction in mean absolute error (MAE). Substantial improvements were also observed in mean squared error, root mean squared error, and mean absolute percentage error, alongside a 7–33 increase in the coefficient of determination (). Furthermore, the model exhibits strong potential for microstructural simulation applications. Overall, the study confirms the effectiveness of the LSGWO-BP model in materials science, especially in enhancing phase-field modeling efficiency and enabling accurate, intelligent prediction for multicomponent alloy systems, thereby offering robust support for microstructure prediction and control.