Learning latent variable evolution for the functional renormalization group

We perform a data-driven dimensionality reduction of the 4-point vertex function characterizing the functional Renormalization Group (fRG) flow for the widely studied two-dimensional t-t' Hubbard model on the square lattice. We show that a deep learning architecture based on a Neural Ordinary Differential Equations efficiently learns the evolution of low-dimensional latent variables in all relevant magnetic and d-wave superconducting regimes of the Hubbard model. Ultimately, our work uses an encoder-decoder architecture to extract compact representations of the 4-point vertex functions for correlated electrons, a goal of utmost importance for the success of cutting-edge methods for tackling the many-electron problem.