Asteroid gravitational field calculation via GeodesyNets with quadratic layers

Asteroid gravity inversion is a method used to infer the internal density distribution of small celestial bodies through external gravitational measurements. In recent years, gravity inversion techniques based on neural networks have seen rapid development, such as GeodesyNet, which utilizes a fully connected SIREN neural network. The traditional SIREN neural network performs well in capturing low-frequency features, such as regular shapes or large-scale density distributions. However, it has limitations in learning high frequency features when processing irregular shapes or abrupt changes in the inner density field. This study introduces an optimized architecture that synergistically integrates SIREN networks with quadratic neurons to augment the SIREN network’s capability in capturing high-frequency gravitational features of asteroids, which seeks to improve the accuracy and stability of inversion processes within the GeodesyNet framework. Eros, Itokawa, 67P/Churyumov-Gerasimenko, and Bennu are selected for testing and evaluation. The results indicate that the density distributions computed by this combined network are more in line with the actual conditions. The maximum relative root mean square error (relRMSE) for homogeneous test models decreased by 6.1% for 67P, and through differential training, the maximum relRMSE for non-homogeneous asteroid surfaces was reduced by 3.0% for Bennu. Moreover, the improvement from GeodesyNetsQ is larger when fewer iterations, and thus fewer data points are used, which will be more helpful to be applied in practical asteroid missions with limited measurements.