Data-driven methods for electron-phonon physics*

Data-driven techniques have emerged as an exciting frontier in scientific computing. In this talk, I will show how these methods can advance precise calculations of electron interactions and dynamics in materials. First, I will show an approach based on singular value decomposition to compress the large datasets representing electron-phonon (e-ph) coupling in first-principles calculations. This approach reveals the inherent low dimensionality of e-ph interactions and enables a speed up by two orders of magnitude in state-of-the-art calculations of properties related to e-ph physics, including charge mobility, spin relaxation, superconducting Tc and band renormalization. Second, I will show how the dynamic mode decomposition technique can accelerate calculations of nonequilibrium electron dynamics in the presence of e-ph collisions and reveal the dominant patterns governing excited electron equilibration and time-domain spectroscopies. Finally, I will discuss how these methods can advance precise many-body physics, showing diagrammatic Monte Carlo calculations that include e-ph diagrams to all orders by leveraging the compressed e-ph interactions. This approach sets a gold standard for e-ph physics and provides nearly exact results for polaron energies and dynamics. Extensions of these data-driven techniques to other interactions in condensed matter will be discussed.