Analytical equations for thermal and electrical conductivity prediction in as-cast magnesium alloys: A symbolic regression approach

The thermal and electrical conductivities of magnesium alloys are highly sensitive to composition and microstructure, with thermal conductivity varying by up to 20-fold across different as-cast alloy systems, making rapid and accurate prediction crucial for high-throughput screening and development of high-performance alloys. This study introduces a physics-informed symbolic regression approach that addresses the limitations of traditional methods, including the high computational cost of first-principles calculations and the poor interpretability of machine learning models. Comprehensive datasets comprising 1512 data points from 60 literature sources were analyzed, including thermal conductivity measurements from 52 alloy systems and electrical conductivity measurements from 36 systems. The derived symbolic regression model achieved Mean Absolute Percentage Errors (MAPEs) of 11.2 % and 11.4 % for thermal conductivity in low and high-component systems, respectively. When integrated with the Smith-Palmer equation, electrical conductivity predictions reached MAPEs of 15.6 % and 16.4 %. Independent validation on an entirely separate dataset of 554 data points from 53 additional literature sources, including 37 previously unseen alloy systems, confirmed model generalizability with MAPEs of 10.7 %−15.2 %. Shapley Additive Explanations (SHAP) analysis was employed to evaluate the relative importance of different features affecting conductivity, while equation decomposition quantified the contribution of individual functional terms. This methodology bridges data-driven prediction with mechanistic understanding, establishing a foundation for knowledge-based design of magnesium alloys with tailored transport properties.