First-principles calculations of electron interactions in materials have seen rapid progress in recent years, with electron-phonon ($e\text{−}\mathrm{ph}$) interactions being a prime example. However, these techniques use large matrices encoding the interactions on dense momentum grids, which reduces computational efficiency and obscures interpretability. For $e\text{−}\mathrm{ph}$ interactions, existing interpolation techniques leverage locality in real space, but the high dimensionality of the data remains a bottleneck to balance cost and accuracy. Here we show an efficient way to compress $e\text{−}\mathrm{ph}$ interactions based on singular value decomposition (SVD), a widely used matrix and image compression technique. Leveraging (un)constrained SVD methods, we accurately predict material properties related to $e\text{−}\mathrm{ph}$ interactions—including charge mobility, spin relaxation times, band renormalization, and superconducting critical temperature—while using only a small fraction (1%–2%) of the interaction data. These findings unveil the hidden low-dimensional nature of $e\text{−}\mathrm{ph}$ interactions. Furthermore, they accelerate state-of-the-art first-principles $e\text{−}\mathrm{ph}$ calculations by about 2 orders of magnitude without sacrificing accuracy. Our Pareto-optimal parametrization of $e\text{−}\mathrm{ph}$ interactions can be readily generalized to electron-electron and electron-defect interactions, as well as to other couplings, advancing quantitative studies of condensed matter.

中文翻译：

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电子声子相互作用的数据驱动压缩

近年来，材料中电子相互作用的第一原理计算取得了快速进展，其中电子-声子（$e\text{-}\mathrm{酸碱度}$）交互就是一个很好的例子。然而，这些技术使用大型矩阵来编码密集动量网格上的相互作用，这降低了计算效率并模糊了可解释性。为了$e\text{-}\mathrm{酸碱度}$为了实现交互，现有的插值技术利用了真实空间中的局部性，但数据的高维性仍然是平衡成本和准确性的瓶颈。这里我们展示一种有效的压缩方法$e\text{-}\mathrm{酸碱度}$基于奇异值分解（SVD）的交互，奇异值分解是一种广泛使用的矩阵和图像压缩技术。利用（无）约束 SVD 方法，我们准确预测与$e\text{-}\mathrm{酸碱度}$相互作用——包括电荷迁移率、自旋弛豫时间、能带重正化和超导临界温度——同时仅使用相互作用数据的一小部分（1%–2%）。这些发现揭示了隐藏的低维性质$e\text{-}\mathrm{酸碱度}$互动。此外，他们加速了最先进的第一原理$e\text{-}\mathrm{酸碱度}$在不牺牲精度的情况下，计算量提高了约 2 个数量级。我们的帕累托最优参数化$e\text{-}\mathrm{酸碱度}$相互作用可以很容易地推广到电子-电子和电子-缺陷相互作用，以及其他耦合，从而推进凝聚态物质的定量研究。