  We consider end-to-end learning approaches for inverse problems of
gravimetry. Due to ill-posedness of the inverse gravimetry, the reliability of
learning approaches is questionable. To deal with this problem, we propose the
strategy of learning on the correct class. The well-posedness theorems are
employed when designing the neural-network architecture and constructing the
training set. Given the density-contrast function as a priori information, the
domain of mass can be uniquely determined under certain constrains, and the
domain inverse problem is a correct class of the inverse gravimetry. Under this
correct class, we design the neural network for learning by mimicking the
level-set formulation for the inverse gravimetry. Numerical examples illustrate
that the method is able to recover mass models with non-constant density
contrast.
