  We present a general framework for the efficient simulation of realistic
fermionic systems with modern machine learning inspired representations of
quantum many-body states, towards a universal tool for ab initio electronic
structure. These machine learning inspired ansatzes have recently come to the
fore in both a (first quantized) continuum and discrete Fock space
representations, where however the inherent scaling of the latter approach for
realistic interactions has so far limited practical applications. With
application to the 'Gaussian Process State', a recently introduced ansatz
inspired by systematically improvable kernel models in machine learning, we
discuss different choices to define the representation of the computational
Fock space. We show how local representations are particularly suited for
stochastic sampling of expectation values, while also indicating a route to
overcome the discrepancy in the scaling compared to continuum formulated
models. We are able to show competitive accuracy for systems with up to 64
electrons, including a simplified (yet fully ab initio) model of the Mott
transition in three-dimensional hydrogen, indicating a significant improvement
over similar approaches, even for moderate numbers of configurational samples.
