Decoding physical mechanisms governing elastic moduli in inorganic materials through interpretable machine learning

Abstract

Rational design of inorganic materials with targeted elastic properties requires understanding the physical mechanisms governing shear modulus (G) and bulk modulus (K). However, current machine learning approaches suffer from model opacity and neglect of feature interactions. Herein, we develop an interpretable machine learning framework that identifies 34 key physical descriptors from 5272 initial features (<1%), achieving R² = 0.892 for G and 0.949 for K with robustness confirmed across diverse model architectures, while revealing their distinct physical origins through comprehensive interpretability analysis integrating ANOVA, SHAP, and partial dependence methods. Our analysis demonstrates that K is primarily governed by geometric and density features reflecting resistance to uniform compression, whereas G is controlled by electronic structure features encoding directional bonding characteristics. Volume per atom (vpa) emerges as the dominant descriptor, with fermi energy (efermi) exhibiting differential sensitivity between moduli (117% relative change for G versus 47% for K). Notably, systematic investigation of feature interactions uncovers synergistic and compensatory effects: low vpa provides the geometric prerequisite for effective orbital overlap, while high efermi ensures sufficient bonding electrons; the density-volume compensation offers alternative pathways to equivalent bulk modulus. These insights are translated into design strategies: high-toughness materials benefit from high-density constituents with moderate Fermi energy, whereas superhard materials demand minimized vpa coupled with maximized efermi. This framework bridges data-driven predictions with solid-state physics, providing a physically interpretable basis for tailoring elastic properties of inorganic materials.