Citation:  Guanghui Cai, Zhendong Cao, Fankai Xie, Huaxian Jia, Wei Liu, Yaxian Wang, Feng Liu, Xinguo Ren, Sheng Meng, Miao Liu. Predicting structuredependent Hubbard U parameters via machine learning[J]. Materials Futures, 2024, 3(2): 025601. doi: 10.1088/27525724/ad19e2 
DFT + U is a widely used treatment in the density functional theory (DFT) to deal with correlated materials that contain openshell 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 and structure is nontrivial and computationally intensive, because the U value has generally a strong chemical and structural dependence. In this work, we address this issue by building a machine learning (ML) model that enables the prediction of material and structurespecific U values at nearly no computational cost. Using Mn–O system as an example, the ML model is trained by calibrating DFT + U electronic structures with the hybrid functional results of more than 3000 structures. The model allows us to determine an accurate U value (MAE = 0.128 eV, R^{2} = 0.97) for any given Mn–O structure. Further analysis reveals that M–O bond lengths are key local structural properties in determining the U value. This approach of the ML U model is universally applicable, to significantly expand and solidify the use of the DFT + U method.
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