Prediction of Curie Temperature in Li-Based Ferrites Using Machine Learning and SHAP Interpretation
Yalin Wang
Extreme Condition Material Properties Science and Technology Center, School of Mathematics and Physics, Southwest University of Science and Technology, Mianyang 621010, China.
Minjiang Dan *
Extreme Condition Material Properties Science and Technology Center, School of Mathematics and Physics, Southwest University of Science and Technology, Mianyang 621010, China.
Xiaoru Liu
Extreme Condition Material Properties Science and Technology Center, School of Mathematics and Physics, Southwest University of Science and Technology, Mianyang 621010, China.
Bin Xie
Southwest Institute of Applied Magnetics, Mianyang 621010, China.
Siyu Song
Extreme Condition Material Properties Science and Technology Center, School of Mathematics and Physics, Southwest University of Science and Technology, Mianyang 621010, China.
Xuan Liu
Extreme Condition Material Properties Science and Technology Center, School of Mathematics and Physics, Southwest University of Science and Technology, Mianyang 621010, China.
Mao Yang
Extreme Condition Material Properties Science and Technology Center, School of Mathematics and Physics, Southwest University of Science and Technology, Mianyang 621010, China.
Zhengwei Xiong
Extreme Condition Material Properties Science and Technology Center, School of Mathematics and Physics, Southwest University of Science and Technology, Mianyang 621010, China and Sichuan Civil-Military Integration Institute, Mianyang 621010, China.
Desheng Pan *
Southwest Institute of Applied Magnetics, Mianyang 621010, China.
Xin Ma *
Extreme Condition Material Properties Science and Technology Center, School of Mathematics and Physics, Southwest University of Science and Technology, Mianyang 621010, China.
Zhipeng Gao
Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, China.
*Author to whom correspondence should be addressed.
Abstract
Li-based ferrites are promising candidates for microwave devices, magnetic functional materials and electronic components due to their high electrical resistivity, excellent high-frequency magnetic response and magnetism tunability via ionic substitution. Curie temperature (TC) determines the thermal stability and service temperature window of ferrites. Nevertheless, TC is comprehensively modulated by stoichiometric ratios, transition and rare-earth ion doping and multi-element synergistic effects, forming complicated nonlinear composition-property relationships that cannot be well captured by traditional empirical methods. Herein, a dataset of Curie temperature for Li-based ferrites is built using 104 experimental data points extracted from published literature. Nine regression models including Lasso, Ridge, multilayer perceptron (MLP), support vector regression (SVR), k-nearest neighbors (KNN), classification and regression tree (CART), XGBoost, random forest (RF) and CatBoost are implemented and compared to predict TC . The SHAP approach is further adopted to quantify the contribution of compositional descriptors to TC . Results reveal that regularized linear models exhibit favorable generalization stability with limited samples. Specifically, the Lasso model achieves the best prediction performance, with a lower MAE of 19.8515, an RMSE of 28.3568, and a high R2 of 0.9404 on the test set. While sophisticated nonlinear models possess strong fitting capacity, several algorithms suffer from obvious error oscillation and unstable predictions on partial samples. SHAP analysis identifies Mg2+, composition variable Mn2+,Fe3+, Ti4+ and Zn2+ as primary features governing TC . Feature dependence curves demonstrate that substitution of nonmagnetic or weakly magnetic ions suppresses superexchange and reduces TC , whereas increased Fe3+ content strengthens magnetic coupling. This work provides systematic and feasible data-driven framework for rapid, macroscopic TC prediction, key-component identification, and subsequent composition optimization of Li-based ferrites.
Keywords: Li-based ferrites, curie temperature, machine learning, regression prediction, SHAP interpretation, compositional design