Development and validation of iron loss prediction model for non-oriented electrical steel based on physics-informed machine learning

To evaluate the key factors influencing on the iron loss of non-oriented electrical steels (NOES) and predict their properties, Physics-Informed Machine Learning (PIML) theory combined with the XGBoost algorithm was employed to develop a NOES-PIML iron-loss prediction model, which integrates physics-based empirical formulas for calculating resistivity and density. The model was further optimized through inverse optimization using the Particle Swarm Optimization (PSO) algorithm to obtain chemical compositions and annealing temperature combinations to reduce iron loss of NOES. A dataset of 600 samples containing chemical composition, annealing temperature and magnetic properties was used for model training and validation. Incorporating physical features such as resistivity and density significantly enhanced the model performance, and the coefficient of determination R ² is 0.98, which indicated a 5% improvement compared with those without physical features. Experimental results and predicted values were compared before and after the introduction of physical features, and residual distribution analysis confirmed that their physical features improved model convergence and prediction accuracy. The interpretability of the model was further analyzed using SHapley Additive exPlanations (SHAP) theory, which revealed the contribution of individual features to model prediction. Then, NOES used for validating the model were prepared based on the chemical compositions and annealing temperature obtained from the optimized results. The iron loss of the finished steel was 3.82 W/kg with a decrease of 6.4% compared with the predicted value. Both iron loss and magnetic induction of the steels were superior to those of similar products specified in the standards, confirming the accuracy and practical applicability of the prediction model. The results demonstrated that NOES-PIML can provide accurate prediction for iron loss using small datasets and be used to design new products or predict their properties.