Abstract 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.

中文翻译：

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使用穷举变量选择的含水熔体-橄榄石平衡的热力学模型

摘要 硅酸盐熔体中的水会影响含水熔体系统的相关系。鉴于水在硅酸盐熔体中的重要性，对含水熔体的非理想性的定量热力学理解对于正确模拟天然岩浆过程是必要的。本文提出了一种定量热力学建模的新方法，用于含水熔体-橄榄石平衡。具体来说，机器学习方法，穷举变量选择 (ES)，用于模拟含水熔体的非理想性。使用ES方法，我们对所有可能的变量组合的预测能力进行定量验证，然后采用预测能力最高的组合作为最优模型方程。ES 方法使我们能够获得含水熔体-橄榄石系统的基本热力学关系，例如不同变量对热力学平衡的相对重要性，以及构建稳健的广义模型。我们表明，熔体总水浓度的线性项和平方项的组合对于描述含水熔体-橄榄石平衡很重要。这个结果是根据与硅酸盐熔体中水的离解相关的微观结构变化来解释的。使用最佳模型的计算再现了水对橄榄石液相线的实验确定的影响以及橄榄石和含水熔体之间 Mg 的分配系数。我们的研究表明，ES 方法产生了一个热力学平衡模型，该模型捕获了解释高维和复杂实验数据的基本热力学关系。