AI 中文总结
该研究针对关联材料中哈伯德相互作用参数预测的成本瓶颈，结合集成学习与蛮力搜索方法，构建了可精准预测过渡金属氧化物cRPA衍生哈伯德参数的高效模型，兼具精度与物理可解释性。
AI 中文摘要
准确确定哈伯德相互作用参数对于关联材料中DFT+$U$、DFT+DMFT、DFT+$U$+$V$等超越密度泛函理论（DFT）的方法至关重要。但实际应用中，这些参数常凭经验选取，限制了其跨材料的可迁移性。约束随机相位近似（cRPA）等先进计算方法为评估哈伯德相互作用提供了严格途径，但其计算成本仍是大规模材料筛选的瓶颈。本文提出用于预测cRPA衍生哈伯德相互作用参数的机器学习（ML）模型，即针对过渡金属氧化物（TMOs）的有效 onsite $U_{\rm eff}$、位点间$V$和洪德耦合$J$。我们将集成学习模型与基于回归的蛮力搜索（BFS）方法结合，以同时实现预测精度和显式解析表达式。构建了涵盖电子、结构和原子性质的特征，包括TM-$d$带宽和TM-$d$/O-$p$带中心间距，作为定位和屏蔽的物理动机描述符。我们的集成模型对$U_{\rm eff}$、$V$和$J$的均方根误差（RMSE）分别为0.148 eV、0.062 eV和0.007 eV。推导的解析形式直接将$U_{\rm eff}$与电子定位及TM-$d$/O-$p$杂化关联，表明杂化和结构紧凑性在确定$V$中的重要性，且显示$J$主要由TM离子的元素描述符决定。综上，本研究提供了一种预测cRPA衍生$U_{\rm eff}$、$V$和$J$的高效方法，同时为这些哈伯德相互作用的潜在因素提供了物理见解。
英文摘要
Accurate determination of Hubbard interaction parameters is essential for beyond-DFT approaches such as DFT+$U$, DFT+DMFT, and DFT+$U$+$V$ in correlated materials. In practice, however, these parameters are often chosen empirically, limiting their transferability across materials. Advanced computational approaches such as the constrained random-phase approximation (cRPA) provide a rigorous route for evaluating Hubbard interactions, but their computational cost remains a bottleneck for large-scale materials screening. Here, we present machine-learning (ML) models for predicting cRPA-derived Hubbard interaction parameters: effective on-site $U_{\rm eff}$, inter-site $V$, and Hund's coupling $J$ for transition-metal oxides (TMOs). We combine ensemble-learning models with a regression-based brute-force search (BFS) approach to achieve both predictive accuracy and explicit analytical expressions. We construct features that capture electronic, structural, and atomic properties, including the TM-$d$ bandwidth and TM-$d$/O-$p$ band-center separation, as physically motivated descriptors of localization and screening. Our ensemble models achieve RMSEs of 0.148 eV, 0.062 eV, and 0.007 eV for $U_{\rm eff}$, $V$, and $J$, respectively. The derived analytical forms directly relate $U_{\rm eff}$ to electron localization and TM-$d$/O-$p$ hybridization, suggest the importance of hybridization and structural compactness in determining $V$, and indicate that $J$ is governed primarily by elemental descriptors of the TM ion. Together, the present study provides an efficient approach for predicting cRPA-derived $U_{\rm eff}$, $V$, and $J$, while offering physical insight into the factors underlying these Hubbard interactions.
