  We introduce a message-passing-neural-network-based wave function Ansatz to
simulate extended, strongly interacting fermions in continuous space. Symmetry
constraints, such as continuous translation symmetries, can be readily embedded
in the model. We demonstrate its accuracy by simulating the ground state of the
homogeneous electron gas in three spatial dimensions at different densities and
system sizes. With orders of magnitude fewer parameters than state-of-the-art
neural-network wave functions, we demonstrate better or comparable ground-state
energies. Reducing the parameter complexity allows scaling to $N=128$
electrons, previously inaccessible to neural-network wave functions in
continuous space, enabling future work on finite-size extrapolations to the
thermodynamic limit. We also show the Ansatz's capability of quantitatively
representing different phases of matter.
