Thermodynamic modeling of hydrous-melt-olivine equilibrium using exhaustive variable selection

Water in silicate melt influences the phase relations of a hydrous-melt system. Given the importance of water in silicate melts, a quantitative thermodynamic understanding of the non-ideality of hydrous melt is necessary to properly model natural magmatic processes. This paper presents a novel method for quantitative thermodynamic modeling of hydrous-melt-olivine equilibrium. Specifically, a machine learning method, exhaustive variable selection (ES), is used to model the non-ideality of hydrous melts. Using the ES method, we quantitatively validate the predictive capacities of all possible combinations of variables and then adopt the combination with the highest predictive capacity as the optimal model equation. The ES method allows us to obtain the underlying thermodynamic relationship of the hydrous-melt-olivine system, such as the relative importance of different variables to the thermodynamic equilibrium, as well as to construct a robust and generalized model. We show that the combination of a linear term and a squared term of the total water concentration of melt is significant for describing the hydrous-melt-olivine equilibrium. This result is interpreted in terms of the microstructural changes related to the dissociation of water in silicate melt. Calculations using the optimal model reproduce the experimentally determined effects of water on the olivine liquidus and the distribution coefficient for Mg between olivine and hydrous melt. Our study demonstrates that the ES method yields a thermodynamic equilibrium model that captures the essential thermodynamic relationship explaining the high-dimensional and complex experimental data.