  We present a novel approach based on artificial neural networks, so-called
geodesyNets, and present compelling evidence of their ability to serve as
accurate geodetic models of highly irregular bodies using minimal prior
information on the body. The approach does not rely on the body shape
information but, if available, can harness it. GeodesyNets learn a
three-dimensional, differentiable, function representing the body density,
which we call neural density field. The body shape, as well as other geodetic
properties, can easily be recovered. We investigate six different shapes
including the bodies 101955 Bennu, 67P Churyumov-Gerasimenko, 433 Eros and
25143 Itokawa for which shape models developed during close proximity surveys
are available. Both heterogeneous and homogeneous mass distributions are
considered. The gravitational acceleration computed from the trained
geodesyNets models, as well as the inferred body shape, show great accuracy in
all cases with a relative error on the predicted acceleration smaller than 1\%
even close to the asteroid surface. When the body shape information is
available, geodesyNets can seamlessly exploit it and be trained to represent a
high-fidelity neural density field able to give insights into the internal
structure of the body. This work introduces a new unexplored approach to
geodesy, adding a powerful tool to consolidated ones based on spherical
harmonics, mascon models and polyhedral gravity.
