使用等变神经网络机器学习Hubbard参数
Machine learning Hubbard parameters with equivariant neural networks
AI总结：
提出一种基于等变神经网络的机器学习模型，利用原子占据矩阵预测DFT+$U$+$V$中的Hubbard参数，在12种材料上实现3%和5%的低误差，大幅加速高精度材料发现与设计。
摘要：
带有扩展Hubbard泛函的密度泛函理论（DFT+$U$+$V$）提供了一个稳健的框架，能够准确描述包含过渡金属或稀土元素的复杂材料。它通过缓解半局域泛函固有的自相互作用误差来实现这一点，这些误差在具有部分填充的d和f电子态的系统中尤为明显。然而，在该方法中实现准确性取决于对同位$U$和异位$V$ Hubbard参数的准确确定。在实践中，这些参数要么通过需要先验知识的半经验调整来获得，要么更准确地通过使用具有预测性但昂贵的从头算计算来获得。在这里，我们提出了一种基于等变神经网络的机器学习模型，该模型使用原子占据矩阵作为描述符，直接捕获系统的电子结构、局部化学环境和氧化态。我们的目标是预测通过密度泛函微扰理论（DFPT）中实现的迭代线性响应计算以及结构弛豫自洽计算出的Hubbard参数。值得注意的是，当在涵盖各种晶体结构和成分的12种材料的数据上进行训练时，我们的模型对Hubbard $U$和$V$参数分别实现了3%和5%的平均绝对相对误差。通过规避计算昂贵的DFT或DFPT自洽协议，我们的模型以可忽略的计算开销显著加速了Hubbard参数的预测，同时接近DFPT的精度。此外，由于其强大的可迁移性，该模型通过高通量计算促进了加速的材料发现和设计，对各种技术应用具有相关性。
英文摘要：
Density-functional theory with extended Hubbard functionals (DFT+$U$+$V$) provides a robust framework to accurately describe complex materials containing transition-metal or rare-earth elements. It does so by mitigating self-interaction errors inherent to semi-local functionals which are particularly pronounced in systems with partially-filled d and f electronic states. However, achieving accuracy in this approach hinges upon the accurate determination of the on-site $U$ and inter-site $V$ Hubbard parameters. In practice, these are obtained either by semi-empirical tuning, requiring prior knowledge, or, more correctly, by using predictive but expensive first-principles calculations. Here, we present a machine learning model based on equivariant neural networks which uses atomic occupation matrices as descriptors, directly capturing the electronic structure, local chemical environment, and oxidation states of the system at hand. We target here the prediction of Hubbard parameters computed self-consistently with iterative linear-response calculations, as implemented in density-functional perturbation theory (DFPT), and structural relaxations. Remarkably, when trained on data from 12 materials spanning various crystal structures and compositions, our model achieves mean absolute relative errors of 3% and 5% for Hubbard $U$ and $V$ parameters, respectively. By circumventing computationally expensive DFT or DFPT self-consistent protocols, our model significantly expedites the prediction of Hubbard parameters with negligible computational overhead, while approaching the accuracy of DFPT. Moreover, owing to its robust transferability, the model facilitates accelerated materials discovery and design via high-throughput calculations, with relevance for various technological applications.
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