Recent advances in modeling density distributions, so-called neural density fields, can accurately describe the density distribution of celestial bodies without, e.g., requiring a shape model - properties of great advantage when designing trajectories close to these bodies. Previous work introduced this approach, but several open questions remained. This work investigates neural density fields and their relative errors in the context of robustness to external factors like noise or constraints during training, like the maximal available gravity signal strength due to a certain distance exemplified for 433 Eros and 67P/Churyumov-Gerasimenko. It is found that both models trained on a polyhedral and mascon ground truth perform similarly, indicating that the ground truth is not the accuracy bottleneck. The impact of solar radiation pressure on a typical probe affects training neglectable, with the relative error being of the same magnitude as without noise. However, limiting the precision of measurement data by applying Gaussian noise hurts the obtainable precision. Further, pretraining is shown as practical in order to speed up network training. Hence, this work demonstrates that training neural networks for the gravity inversion problem is appropriate as long as the gravity signal is distinguishable from noise. Code and results are available at https://github.com/gomezzz/geodesyNets

该研究研究了神经密度场及其对外部因素（如噪声或约束）的鲁棒性，研究表明预训练有助于加快网络训练，同时证明训练神经网络用于重力反演问题是合适的，只要重力信号能够与噪声区分开来。

神经密度场的鲁棒性研究