Adaptive energy reference for machine-learning models of the electronic density of states

The electronic density of states (DOS) provides information regarding the distribution of electronic states in a material, and can be used to approximate its optical and electronic properties and therefore guide computational material design. Given its usefulness and relative simplicity, it has been one of the first electronic properties used as target for machine-learning approaches going beyond interatomic potentials. A subtle but important point, well-appreciated in the condensed matter community but usually overlooked in the construction of data-driven models, is that for bulk configurations the absolute energy reference of single-particle energy levels is ill-defined. Only energy differences matter, and quantities derived from the DOS are typically independent on the absolute alignment. We introduce an adaptive scheme that optimizes the energy reference of each structure as part of training, and show that it consistently improves the quality of ML models compared to traditional choices of energy reference, for different classes of materials and different model architectures. On a practical level, we trace the improved performance to the ability of this self-aligning scheme to match the most prominent features in the DOS. More broadly, we believe that this work highlights the importance of incorporating insights into the nature of the physical target into the definition of the architecture and of the appropriate figures of merit for machine-learning models, that translate in better transferability and overall performance.
This record contains all the necessary data files and scripts to support the results presented in the paper with the same title.

电子态密度（DOS）揭示了材料中电子状态的分布情况，并可用于近似其光学与电子性质，从而指导计算材料设计。鉴于其重要性及相对简便性，电子态密度已成为超越原子间势能的机器学习方法的早期目标之一。在凝聚态物理领域广为人知但常在数据驱动模型构建中被忽视的一个微妙而重要的观点是，对于体相配置，单粒子能级的绝对能量参照是不确定的。只有能量差是重要的，由电子态密度推导出的量通常独立于绝对对齐。我们提出了一种自适应方案，该方案在训练过程中优化每个结构的能量参照，并证实相较于传统的能量参照选择，该方案在提升不同材料和不同模型架构的机器学习模型质量方面具有一致性。从实际层面来看，我们追溯了这种自我对齐方案能够匹配电子态密度中最显著特征的能力，从而提高了性能。更广泛地，我们认为这项工作突显了将物理目标的本质洞察融入机器学习模型架构及其适当评价指标定义的重要性，这转化为更好的迁移性和整体性能。本记录包含了支持论文中呈现结果的所有必要数据文件和脚本。