Explainable Multi-Target Machine Learning Framework for Predicting Thermophysical Properties of Chemical Elements Using Periodic Table Descriptors

Abstract

The thermophysical properties of the chemical elements underpin materials selection, process design, and fundamental chemistry, yet their experimental determination remains difficult for rare, radioactive, or synthetic species. This study develops an explainable, multi-target machine learning framework that predicts four key properties, namely melting point, boiling point, density, and atomic radius, directly from readily available periodic-table descriptors. Twelve descriptors, including atomic number, atomic mass, period, group, electronegativity, ionization energy, electron affinity, and valence-shell electron counts derived from electron configurations, were compiled for the elements. Eight regression algorithms spanning linear, kernel, instance-based, and tree-ensemble families were systematically benchmarked using repeated five-fold cross-validation, with all targets modeled on a natural-logarithmic scale and missing descriptors handled by leakage-free iterative imputation. Tree-based ensembles considerably outperformed the linear models, which did not account for the nonlinear nature of the periodic relationships. The best mean performance was provided by the Extra Trees algorithm, which served as the framework base learner. After optimization, the framework reached coefficients of determination of 0.72, 0.76, 0.88, and 0.74 for the melting point, boiling point, density, and atomic radius, respectively, alongside low values of root-mean-square error. Model behavior was interpreted using Shapley additive explanations and permutation importance. Ionization energy emerged as the dominant descriptor for melting point, boiling point, and density owing to its correlation with bonding strength and electron localization, whereas the period governed atomic radius in line with the shell structure. The largest prediction errors were associated with elements exhibiting anomalous bonding (such as carbon, boron, and phosphorus) and strong relativistic effects (such as gold and mercury).