Data-Driven Compression of Electron-Phonon Interactions

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.