A formalism is presented for the construction of multicomponent lattice gas models parameterized with ab initio (typically density functional theory) data. The leave-multiple-out and the leave-one-out cross validation score are showcased, and practical algorithms are developed and implemented in a new code called the Ab initio Mean-field Augmented Lattice Gas Modeling (AMALGM) code. The functionality of these algorithms is demonstrated with a fully worked out example using the O/Fe(100) system. AMALGM and the formalism on which it is based are envisioned as a surface-oriented lattice gas alternative to other cluster expansion codes that are typically geared toward bulk systems whose lateral interactions between components are parameterized using an Ising model. While the formalism is created within the context of surfaces, it is equally applicable to bulk materials.

中文翻译：

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从头算数据参数化的多组分晶格气模型群扩展的公式化：从头算平均场增强的晶格气建模代码简介

提出了用从头算（通常是密度泛函理论）数据进行参数化的多组分晶格气体模型构造的形式化方法。展示了留多出和留一出交叉验证得分，并且在称为“从头算平均场增强晶格气体建模”（AMALGM）的新代码中开发并实现了实用算法。使用O / Fe（100）系统的完整示例演示了这些算法的功能。AMALGM及其所基于的形式主义被设想为一种面向表面的晶格气，可以替代通常适用于散装系统的其他簇扩展代码，这些散装系统的组件之间的横向相互作用使用伊辛模型进行了参数化。虽然形式主义是在表面环境中创建的，