Understanding the fundamental mechanisms of thermal expansion in high-entropy ceramics is crucial for their structural applications under extreme conditions. Here, we propose a machine learning (ML)-driven approach to reveal the different underlying mechanisms that govern the thermal expansion in high-entropy carbides (HECs) and high-entropy diborides (HEBs). Molecular dynamics simulations based on the well-fitted neuroevolution potentials are used to effectively collect the coefficient of thermal expansion (CTE) data of HECs and HEBs, and features with three levels, including the atomic level, the monolithic level, and the high-entropy level, are simultaneously considered to achieve reliable ML training. Five descriptors within a Linear Regression model are derived as the optimal combination for the accurate CTE prediction in HECs, where lattice distortion and its variation under temperature are revealed to have the dominant influence on suppressing the thermal expansion of HECs by strengthening ionic bonding and alleviating anharmonic effects. Conversely, the optimal combination of descriptors for the precise CTE prediction in HEBs is exclusively linked to fundamental parameters at both atomic and monolithic levels, highlighting the cocktail effects in impacting CTEs of HEBs. This work proposes an efficient framework for mechanism revelation by ML to facilitate the rational design of high-entropy ceramics with desired properties.

Herein we establish formation ability descriptors of high-entropy rare-earth monosilicates (HEREMs) via the data-driven discovery based on the high-throughput solid-state reaction and machine learning (ML) methods. Specifically, adequate high-quality data are generated with 132 samples synthesized by the self-developed high-throughput solid-state reaction apparatuses, and 30 potential descriptors are considered in ML simultaneously. Two classifications are proposed to study the phase formation of HEREMs via the ML approach combined with the genetic algorithm: (Ⅰ) to distinguish pure HEREMs (X) from other phases and (Ⅱ) to categorize the detail phases of HEREMs (X2, X1, or X2+X1). Four formation ability descriptors ( $\overline{r_{\mathrm{M}\mathrm{e}}}$, $\overline{E_{\mathrm{F}}}$, ${\delta }_{E_{\mathrm{g}}}$, and ${\delta }_{Z^{\ast }}$) with a high validation accuracy (96.2%) are proposed as the optimal combination for Classification Ⅰ, where a smaller $\overline{r_{\mathrm{M}\mathrm{e}}}$ is determined to have the most significant influence on the formation of HEREMs. For Classification Ⅱ, a 100% validation accuracy is achieved by using only two formation ability descriptors ( $\overline{r_{\text{ion }}}$ and ${\delta }_{Z^{\ast }}$), where the $\overline{r_{\text{ion }}}$ is analyzed to be the dominant feature and a lower $\overline{r_{\text{ion }}}$ is beneficial to the formation of X2-HEREMs. Based on our established formation ability descriptors, 6,045 unreported multicomponent silicates are explored, and 3,478 new HEREMs with 2,700 X2-and 423 X1-HEREMs are predicted.