Discovering superhard high-entropy diboride ceramics via a hybrid data-driven and knowledge-enabled model

Materials descriptors with multivariate, multiphase, and multiscale of a complex system have been treated as the remarkable materials genome, addressing the composition–processing–structure–property–performance (CPSPP) relationships during the development of advanced materials. With the aid of high-performance computations, big data, and artificial intelligence technologies, it is still a challenge to derive an explainable machine learning (ML) model to reveal the underlying CPSPP relationship, especially, under the extreme conditions. This work supports a smart strategy to derive an explainable model of composition–property–performance relationships via a hybrid data-driven and knowledge-enabled model, and designing superhard high-entropy diboride ceramics (HEBs) with a cost-effective approach. Five dominate features and optimal model were screened out from 149 features and nine algorithms by ML and validated in first-principles calculations. From Shapley additive explanations (SHAP) and electronic bottom layer, the predicted hardness increases with the improved mean electronegativity and electron work function (EWF) and decreases with growing average d valence electrons of composition. The 14 undeveloped potential superhard HEBs candidates via ML are further validated by first-principles calculations. Moreover, this EWF-ML model not only has better capability to distinguish the differences of solutes in same group of periodic table but is also a more effective method for material design than that of valence electron concentration.