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.

翻译：我们考虑重力测量反问题的端到端学习方法。由于重力测量反问题具有不适定性，学习方法的可靠性存疑。为解决这一问题，我们提出基于正确类的学习策略。在设计神经网络架构和构建训练集时，我们利用适定性定理。在密度对比函数作为先验信息的情况下，质量区域可在特定约束条件下被唯一确定，且区域反问题属于重力测量反问题的正确类。在该正确类框架下，我们通过模拟重力测量反问题的水平集公式来设计用于学习的神经网络。数值实验表明，该方法能够恢复具有非恒定密度对比度的质量模型。