A Hybrid Computational Framework for Mineral Optics via Explainable AI and Symbolic Regression

Abstract

The accurate determination of mineral optical properties faces a persistent trade-off between the high cost of crystallographic characterization and the limited accuracy of classical empirical relationships, such as the Gladstone-Dale law. These empirical methods fail to capture non-linear compositional effects and mechanical influences in complex natural systems. This study addresses these limitations by proposing a novel five-layer computational framework that integrates Explainable Artificial Intelligence (XAI) with Symbolic Regression (PySR). Leveraging a curated dataset of 3,112 mineral samples, we demonstrate that gradient-boosted decision trees, specifically LightGBM, achieve superior predictive accuracy (R 2 = 0.814, RMSE = 0.304) using only basic physicochemical attributes, effectively decoupling prediction from the necessity of Crystallographic Information Files (CIF). Critically, a direct numerical benchmark shows this result surpasses the Gladstone-Dale law applied to the same test set (R 2 = 0.743, RMSE = 0.361). Beyond prediction, SHAP analysis identifies Mohs hardness (mean ∣SHAP∣ = 0.192) as a determinant nearly as critical as specific gravity (mean ∣SHAP∣ = 0.207). Symbolic regression subsequently distills the model into interpretable constitutive equations, discovering a non-linear power law n ∝ H 0.263 and a unified interaction term n ∝ (ρ + H) 0.208 , which extends classical formulations to explicitly incorporate mechanical bond strength. These findings bridge the gap between high-accuracy data-driven modeling and fundamental physical understanding, establishing a robust numerical methodology for materials discovery in computational mineralogy.