Learning on the correct class for domain inverse problems of gravimetry

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.