预测结构依赖的Hubbard U参数：通过机器学习评估杂化泛函级别的交换作用
Predicting structure-dependent Hubbard U parameters for assessing hybrid functional-level exchange via machine learning
AI总结：
本研究构建了一个仅基于结构信息预测材料特定Hubbard U参数的机器学习模型，在Mn-O体系中以极低计算成本实现高精度（MAE=0.128 eV，R²=0.97），并揭示U值主要由局部键长决定，可简化DFT+U方法的应用。
摘要：
DFT+U是密度泛函理论（DFT）中广泛使用的一种处理方法，用于处理含有开壳层元素的关联材料，通过该方法可以在不增加太多计算开销的情况下，修正局域和半局域近似的定量甚至有时是定性的失败。然而，为给定系统找到合适的U参数并非易事，通常需要计算密集且繁琐的第一性原理计算。在本快报中，我们通过构建一个仅从结构信息预测材料特定U参数的机器学习（ML）模型来解决这一问题。我们针对Mn-O化学体系训练了一个ML模型，通过将超过3000个Mn-O结构的DFT+U电子结构与杂化泛函结果进行校准。该模型使我们能够以几乎为零的计算成本，为任何给定结构确定可靠的U值（平均绝对误差MAE=0.128 eV，决定系数R²=0.97）；然而，所获得的U值与通过传统第一性原理方法获得的值一样好。进一步分析表明，U值主要由局部化学结构决定，尤其是键长，而这一特性被本工作中开发的ML模型很好地捕捉。这种ML U模型的概念具有普遍适用性，可以通过提供特定结构、易于获取的U值，大大简化DFT+U方法的使用。
英文摘要：
DFT+U is a widely used treatment in the density functional theory (DFT) to deal with correlated materials that contain open-shell elements, whereby the quantitative and sometimes even qualitative failures of local and semilocal approximations can be corrected without much computational overhead. However, finding appropriate U parameters for a given system is non-trivial and usually requires computationally intensive and cumbersome first-principles calculations. In this Letter, we address this issue by building a machine learning (ML) model to predict material-specific U parameters only from the structural information. An ML model is trained for the Mn-O chemical system by calibrating their DFT+U electronic structures with the hybrid functional results of more than Mn-O 3000 structures. The model allows us to determine a reliable U value (MAE=0.128 eV, R2=0.97) for any given structure at nearly no computational cost; yet the obtained U value is as good as that obtained from the conventional first-principles methods. Further analysis reveals that the U value is primarily determined by the local chemical structure, especially the bond lengths, and this property is well captured by the ML model developed in this work. This concept of the ML U model is universally applicable and can considerably ease the usage of the DFT+U method by providing structure-specific, readily accessible U values.
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