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 (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>e</a:mi><a:mtext>−</a:mtext><a:mrow><a:mi>ph</a:mi></a:mrow></a:mrow></a:math>) 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>e</c:mi><c:mtext>−</c:mtext><c:mrow><c:mi>ph</c:mi></c:mrow></c:mrow></c:math> 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:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>e</e:mi><e:mtext>−</e:mtext><e:mrow><e:mi>ph</e:mi></e:mrow></e:mrow></e:math> 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 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi>e</g:mi><g:mtext>−</g:mtext><g:mrow><g:mi>ph</g:mi></g:mrow></g:mrow></g:math> 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 <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>e</i:mi><i:mtext>−</i:mtext><i:mrow><i:mi>ph</i:mi></i:mrow></i:mrow></i:math> interactions. Furthermore, they accelerate state-of-the-art first-principles <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mi>e</k:mi><k:mtext>−</k:mtext><k:mrow><k:mi>ph</k:mi></k:mrow></k:mrow></k:math> calculations by about 2 orders of magnitude without sacrificing accuracy. Our Pareto-optimal parametrization of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mi>e</m:mi><m:mtext>−</m:mtext><m:mrow><m:mi>ph</m:mi></m:mrow></m:mrow></m:math> interactions can be readily generalized to electron-electron and electron-defect interactions, as well as to other couplings, advancing quantitative studies of condensed matter. Published by the American Physical Society 2024