Physics-Informed neural networks for gravity field modeling incorporating observation, geometry and density constraints

The physics-informed neural networks (PINN) are emerging as a new tool for gravity field modeling. In some scenarios, such as near-source gravitational fields representation, PINN may have greater potential than traditional spherical/ellipsoidal harmonics solutions, as the latter suffers from both theoretical and numerical divergence problems for sources with complex geometry. By incorporating observational, geometrical and statistical density information into the neural network, we aim to reduce the non-uniqueness of the solution space, therefore obtaining improved accuracy in representing gravity fields, especially near the source body. By transforming the trained gravitational potential into density distribution through Poisson's equation, we also provide a new perspective to observe the evolution of the neural network for gravity field modeling as "redistribution of equivalent density sources". The influence of multiple parameters of the neural network on the performance of the PINN gravity modeling, including its size and shape, distribution of Laplacian and Poisson collocation points, and balance between loss functions of the multiple constraints applied, are also investigated. Numerical results are illustrated using the EROS asteroid model and a regional DEM model of Colorado Geoid Experiment area.