  Methods inspired from machine learning have recently attracted great interest
in the computational study of quantum many-particle systems. So far, however,
it has proven challenging to deal with microscopic models in which the total
number of particles is not conserved. To address this issue, we propose a new
variant of neural network states, which we term neural coherent states. Taking
the Fr\"ohlich impurity model as a case study, we show that neural coherent
states can learn the ground state of non-additive systems very well. In
particular, we observe substantial improvement over the standard coherent state
estimates in the most challenging intermediate coupling regime. Our approach is
generic and does not assume specific details of the system, suggesting wide
applications.
