Modeling clinopyroxene-liquid trace element partition coefficients in the upper mantle: pioneering a machine learning approach

Partition coefficients (Ds) are an integral tool for understanding geochemical processes within the deep parts of the mantle. However, their availability is limited due to their challenging experimental determination. Leveraging the power of machine learning (ML) approaches, we developed a model to predict partition coefficients between clinopyroxene and liquid (ranging from anhydrous and hydrous melts to aqueous fluids) for 31 trace elements. The model was trained on experimental data covering pressures from 0.5 to 6 GPa, temperatures of 700 to 1635 °C, and compositions ranging from eclogite to peridotite. The predictive model achieved high accuracy, with an R² = 0.94 and RMSE = 3.77. The five most influential features were temperature, ionic charge, radii, and the clinopyroxene Al₂O₃ and SiO₂ wt%. Our model’s predictive capabilities enabled a detailed investigation of how pressure–temperature-composition conditions impact crystal lattice strain and electrostatic parameters. The model demonstrated that water content in the liquid phase substantially impacts trace element partitioning. As H₂O increases in the liquid phase, the optimum valence in the M2 site increases, while the D₀^Δe=0 in both M2 and M1 sites significantly decreases. To demonstrate our model’s utility, we applied it to calculate trace element patterns of fluids equilibrated with low-temperature metasomatic xenoliths from the Kaapvaal craton. The calculated fluids exhibited ribbed and planar patterns, remarkably similar to those of natural High-Density Fluids (HDFs) found within diamonds from the same geological region. This development advances our understanding of geochemical processes and establishes a powerful ML approach that could develop predictive modeling in complex geological systems.