fig7

Figure 7. Mechanistic interpretability analysis of the Hybrid PIML framework. (A) SHAP summary beeswarm plot. The physics-derived strengthening parameter (LS_term) exhibits a distinct positive correlation with hardness, validating the model’s adherence to SSS principles; (B) Global feature importance ranking. The LS_term is identified as the dominant predictor among all features, confirming that the PIML architecture successfully prioritizes physical mechanisms over raw compositional data; (C) SHAP dependence plot for LS_term. The curve reveals a clear monotonic increasing relationship between the theoretical strengthening factor and predicted hardness, demonstrating the model’s capability to capture the underlying non-linear physical laws. Hybrid PIML: Hybrid physics-informed machine learning; SHAP: SHapley Additive exPlanations; SSS: solid solution strengthening; VEC: valence electron concentration.