Data-driven prediction of hardness and layer behavior in YbSi-mullite-Si environmental barriers.

Environmental barrier coatings (EBCs) on SiC/SiC composites exhibit strong through-thickness heterogeneity arising from phase transitions, layered architectures, and microstructural defects, which can confound conventional per-layer statistical analysis. Here, we present a layer-aware data-driven framework that predicts hardness across the YbSi→mullite→Si→substrate stack using nanoindentation measurements and compositionally decoded layer descriptors. Individual indentation traces are concatenated into a continuous, normalized depth coordinate, enabling coating-scale hardness profiling without requiring perfectly segmented layers. To capture both local mechanics and depth-dependent coupling, we construct physics-aware synthetic descriptors that combine displacement, harmonic contact stiffness, normalized penetration, depth-coupling terms, phase-fraction features, and gradient-based (DIFF) measures. Redundancy in the expanded feature space is reduced via ANOVA-F screening to yield a compact, informative descriptor set. Across four held-out coating motifs (A-D), direct depth-wise hardness prediction with tree-based ensemble learners (XGBRegressor, CatBoost, and LGBM) achieves [Formula: see text] with [Formula: see text]. When the predicted profiles are subsequently processed using within-layer neighborhood averaging, the corresponding post-processed smoothed-profile agreement reaches [Formula: see text] and [Formula: see text]. This post-hoc operation attenuates short-range fluctuations while preserving systematic layer-scale trends; it does not modify the fitted regressors or the original experimental hardness values. When reformulated at the design-relevant resolution of layer means, ensemble models recover layer-level hardness with mean-by-layer [Formula: see text] up to [Formula: see text] and [Formula: see text] on unseen motifs, supporting robust comparison of coating designs. Mechanistic interpretability is provided by SHAP, augmented with hierarchical clustering and graph-community analysis, which highlights coherent feature groups associated with depth transitions and phase-dependent responses. Scientific contribution statement: We introduce an integrated learning pipeline that couples continuous-depth nanoindentation representation with physics-aware descriptors to predict hardness in heterogeneous EBC systems while explicitly accounting for layer composition and stack position. In this framework, layer information is not inferred through a separate classification or segmentation task; instead, categorical layer descriptors are decoded into continuous phase-fraction features and used as model inputs. By demonstrating generalization across unseen coating motifs and by improving design-level (layer-mean) accuracy while retaining depth-wise resolution, the framework enables coating-scale mechanical profiling that is resilient to defects and local variability. Finally, we provide a structured interpretability workflow (SHAP + clustering + graph communities) that links predictive signals to physically meaningful descriptor families, supporting mechanistic insight and materials design decisions.