  We perform a data-driven dimensionality reduction of the scale-dependent
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 demonstrate that a deep learning architecture based on a
Neural Ordinary Differential Equation solver in a low-dimensional latent space
efficiently learns the fRG dynamics that delineates the various magnetic and
$d$-wave superconducting regimes of the Hubbard model. We further present a
Dynamic Mode Decomposition analysis that confirms that a small number of modes
are indeed sufficient to capture the fRG dynamics. Our work demonstrates the
possibility of using artificial intelligence to extract compact representations
of the 4-point vertex functions for correlated electrons, a goal of utmost
importance for the success of cutting-edge quantum field theoretical methods
for tackling the many-electron problem.
