Physics-Informed Neural Networks (PINNs) for gravity field modelling and representation: With application to asteroid EROS

The modeling and representation of gravity field is a fundamental problem in geophysics and geodesy. With the development of modern gravimetry observation technology, it is possible to build ultra-high degree gravity field models for the Earth and other planets. However, existing gravitational field representation models based on spherical/ellipsoidal harmonics encounter convergence problems in the near-surface space, especially in the region between the maximum Bjerhammer sphere and the minimum Brillouin sphere. This is likely to become a bottleneck restricting the further development of extremely-high degree Earth and planetary gravitational field models. Physics informed neural networks (PINNs) has emerging as a promising new framework in solving forward and inverse problems based on partial differential equations in recent years. It offers a new technique for forward and inverse modeling of gravity fields based on Poisson’s equation, as well as providing a new idea for representation of gravity fields using neural networks. This paper briefly introduces the basic principle and some recent improvements of physics informed neural networks, and applies it to the gravitational field modeling of asteroid EROS. Numerical tests prove its availability and superiority in representing gravitational fields caused by complex sources. This work also lays a foundation for future works to model the gravitational field of Earth-like planets based on physics informed neural networks.