arXiv:2507.09001cond-mat.mtrl-scicond-mat.dis-nn2025-07被引 2

电子结构数据冗余高,源于低内在维度,可大幅精简数据集。

Surprisingly High Redundancy in Electronic Structure Data Across Materials Explained by Low Intrinsic Dimensionality

  • 发现电子结构数据具有显著冗余,源于其低内在维度。
  • 随机删减数据后模型精度下降极小,且可减少90%以上数据量。
  • 适合需要高效训练的材料科学与机器学习研究者使用。

基于机器学习的电子结构建模通常依赖于计算成本高昂的Kohn-Sham密度泛函理论生成的大规模数据集,因无法预先判断哪些数据对学习至关重要。本文揭示了多种材料体系中电子结构数据存在显著冗余,并将其归因于数据内在维度低。研究表明,即使随机删减数据,也能在预测精度几乎不变的情况下大幅缩减数据规模。此外,一种基于覆盖范围的剪枝策略可在保持化学精度和模型泛化能力的前提下,将数据量减少两个数量级,训练时间缩短三倍以上。我们进一步证明,关键的电子结构信息存在于一个低维非线性流形上,为数据可剪枝性提供了几何解释。这些发现与‘近似性’观点一致,即局部原子环境主导电子性质,表明大规模数据集可能包含高度重叠的信息。本研究挑战了现有认为需海量数据才能准确预测的假设,为每类材料识别最小代表性数据集指明了路径。

原文摘要 · Abstract (English)

Machine learning (ML) models for electronic structure typically rely on large datasets generated by computationally expensive Kohn-Sham density functional theory calculations, as it is not known a priori which portions of the data are essential for accurate learning. Here, we reveal significant redundancies in electronic structure datasets across diverse material systems and attribute them to the low intrinsic dimensionality of the underlying data. We show that even random pruning can substantially reduce dataset size with minimal degradation in predictive accuracy. Moreover, a state-of-the-art coverage-based pruning strategy that samples data across all learning difficulties preserves chemical accuracy and model generalizability while using up to two orders of magnitude less data and reducing training time by a factor of three or more. We further demonstrate that the essential electronic structure information lies on a low-dimensional, non-linear manifold, providing a geometric explanation for the observed prunability. These observations are consistent with the predominance of local atomic environments in determining electronic properties, as suggested by nearsightedness arguments, and indicate that large-scale datasets may contain highly overlapping information. Our findings challenge the prevailing assumption that such extensive datasets are necessary for accurate ML-based electronic structure predictions and open a path toward identifying minimal, representative datasets for each material class.

机器学习电子结构数据压缩低维流形

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