Explainable machine learning to uncover hydrogen diffusion mechanism in clinopyroxene

Estimating the water content of mantle-derived magma using clinopyroxene (cpx) phenocrysts serves as a valuable constraint on the water budget in deep Earth. Intricate magma processes and the high hydrogen diffusion rate necessitate careful evaluations of whether the water content in cpx preserves its original state. Machine learning (ML) has been utilized to develop a classifier for judging hydrogen diffusion in cpx. Never- theless, the opaqueness and complexity of most ML models hinder a clear understanding of their classification principles. To elucidate the mechanistic basis of the ML model, the Shapley theory is integrated to determine the contributions of major elements of cpx as features in a linear additive manner. This study achieves superior classification performance using an extreme gradient boosting model and innovatively presents a quantitative evaluation of feature importance at the sample level for each observation. The results indicate that Na plays a predominant role in the diffusion process surpassing other major elements and its associated hydrogen can easily diffuse out of cpx. Our model also identifies various hydrogen association modes in different elemental com- positions and puts constraints on the properties of incorporated hydrogen with non-lattice forming elements in cpx. The findings demonstrate that the application of explainable ML methods in mineralogy holds significant potential for advancing the comprehension of geological phenomena.