用流匹配模型高效生成带电材料的电子密度，提升精度且保持化学可用性。
ChargeFlow: Flow-Matching Refinement of Charge-Conditioned Electron Densities
- 基于3D U-Net的流匹配模型，从原子密度叠加重构DFT电子密度
- 在非局域电荷重分布任务上误差降为3.21%，相似度升至0.655
- 适合缺陷、掺杂等带电材料研究，可直接用于后续化学分析
准确的电子密度对电子结构理论至关重要，但使用密度泛函理论计算带电状态相关的密度对大规模筛选和缺陷工作流而言仍过于昂贵。我们提出ChargeFlow，一种基于流匹配的精炼模型，利用3D U-Net速度场将带电条件下的原子密度叠加转换为原生周期性实空间网格上的DFT电子密度。模型在9,502个来自Materials Project的带电体系计算数据上训练，并在包含钙钛矿、带电缺陷、金刚石缺陷、金属有机框架和有机晶体的外部1,671结构基准上评估。ChargeFlow并非在所有同分布类别上均最优，但在以非局域电荷重分布和电荷态外推为主的问题上表现最强，将形变密度误差从3.62%降至3.21%，电荷响应余弦相似度从0.571提升至0.655（相比ResNet基线）。预测密度在下游分析中仍具化学意义，所有1,671个基准结构均成功完成Bader分区，且电势保真度高，表明流匹配是带电材料密度精炼的实用策略。
原文摘要 · Abstract (English)
Accurate charge densities are central to electronic-structure theory, but computing charge-state-dependent densities with density functional theory remains too expensive for large-scale screening and defect workflows. We present ChargeFlow, a flow-matching refinement model that transforms a charge-conditioned superposition of atomic densities into the corresponding DFT electron density on the native periodic real-space grid using a 3D U-Net velocity field. Trained on 9,502 charged Materials Project-derived calculations and evaluated on an external 1,671-structure benchmark spanning perovskites, charged defects, diamond defects, metal-organic frameworks, and organic crystals, ChargeFlow is not uniformly best on every in-distribution class but is strongest on problems dominated by nonlocal charge redistribution and charge-state extrapolation, improving deformation-density error from 3.62% to 3.21% and charge- response cosine similarity from 0.571 to 0.655 relative to a ResNet baseline. The predicted densities remain chemically useful under downstream analysis, yielding successful Bader partitioning on all 1,671 benchmark structures and high-fidelity electrostatic potentials, which positions flow matching as a practical density-refinement strategy for charged materials.
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