  In this work, we use neural quantum states (NQS) to describe the
high-dimensional wave functions of electron-phonon coupled systems. We
demonstrate that NQS can accurately and systematically learn the underlying
physics of such problems through a variational Monte Carlo optimization of the
energy with minimal incorporation of physical information even in highly
challenging cases. We assess the ability of our approach across various lattice
model examples featuring different types of couplings. The flexibility of our
NQS formulation is demonstrated via application to ab initio models
parametrized by density functional perturbation theory consisting of electron
or hole bands coupled linearly to dispersive phonons. We compute accurate
real-frequency spectral properties of electron-phonon systems via a novel
formalism based on NQS. Our work establishes a general framework for exploring
diverse ground state and dynamical phenomena arising in electron-phonon
systems, including the non-perturbative interplay of correlated electronic and
electron-phonon effects in systems ranging from simple lattice models to
realistic models of materials parametrized by ab initio calculations.
