# Investigation of the Robustness of Neural Density Fields

arXiv: https://arxiv.org/abs/2305.19698 · HTML: https://mlsanity.com/paper/2305.19698/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 6 of 6)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Real-Time Optimal Control for Irregular Asteroid Landings Using Deep Neural Networks](https://mlsanity.com/paper/1901.02210/) (2019)
- [Selected Trends in Artificial Intelligence for Space Applications](https://mlsanity.com/paper/2212.06662/) (2022)
- [Geodesy of irregular small bodies via neural density fields: geodesyNets](https://mlsanity.com/paper/2105.13031/) (2021)
- [Target selection for Near-Earth Asteroids in-orbit sample collection missions](https://mlsanity.com/paper/2212.09497/) (2022)
- [Optimization of body configuration and joint-driven attitude stabilization for transformable spacecrafts under solar radiation pressure](https://mlsanity.com/paper/2301.08435/) (2023)

## Built on by (most cited first, 2 of 2)

- [MasconCube: Fast and Accurate Gravity Modeling with an Explicit Representation](https://mlsanity.com/paper/2509.08607/) (2025)
- [Three-dimensional inversion of gravity data using implicit neural representations and scientific machine learning](https://mlsanity.com/paper/2510.17876/) (2025)

## Abstract (arXiv)

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