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Experiments with artificial neural networks and geodesy

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# GeodesyNets
Code to train visualize and evaluate neural density fields using pytorch.

The code was developed and use for the writing of the paper:

> Dario Izzo and Pablo Gomez, "Geodesy of irregular small bodies via neural density fields: geodesyNets". [arXiv:2105.13031](https://arxiv.org/pdf/2105.13031.pdf). (2021).

An extension of this work is provided in the repository [esa/masconCube](https://github.com/esa/masconCube), that served as the codebase for the paper:

> Pietro Fanti and Dario Izzo, "MasconCube: Fast and Accurate Gravity Modeling with an Explicit Representation". [arXiv:2509.08607](https://arxiv.org/pdf/2509.08607). (2025).

## Installation

We recommend using a [conda](https://docs.conda.io/en/latest/) environment to run this code. Once you have conda, (we also strongly suggest mamba istalled on the base environment) you can simply execute the `install.sh` script to create a conda environment called `geodesynet` with all required modules.

Note that to run some of the notebooks you may also need other dependencies.

## Inference

The following script will run the training (non-differential version) for all the homogeneous asteroids in the paper. Changing config you can replicate other paper's results, including ablation studies.

```sh
python run_benchmark.py cfgs/siren_all_runs.toml
```

# Architecture at a glance
A geodesyNet represents the body density directly as a function of Cartesian coordinates. 
Recently, (see https://github.com/bmild/nerf)  a related architecture called Neural Radiance Fields (NeRF) was introduced to represent three-dimensional objects and complex scenes with an impressive accuracy learning from a set of two-dimensional images. The training of a NeRF solves the inverse problem of image rendering as it back-propagates the difference between images rendered from the network and a sparse set of observed images.

Similarly, the training of a geodesyNet solves the gravity inversion problem. The network learns from a dataset of measured gravitational accelerations back-propagating the difference to the corresponding accelerations computed from the density represented by the network.

The overall architecture to learn a neural density field is shown below:

![GeodesyNet Architecture](https://raw.githubusercontent.com/darioizzo/geodesyNets/master/figures/Fig1.png)

# Neural Density Field for 67p Churyumov-Gerasimenko
Once the network is trained we can explore and visualize the neural density field using techniques similar to 3D image scanning. This
results in videos such as the one below, obtained using the gravitational signature of the comet 67p Churyumov-Gerasimenko. Units are non dimensional.

![Neural Density Field for 67p](https://raw.githubusercontent.com/darioizzo/geodesyNets/master/figures/67p_low.gif)

# Neural Density Field for Bennu
Similarly, the video below refers to the results of differential training over a heterogenous Bennu model. Units are non dimensional.

![Neural Density Field for 67p](https://raw.githubusercontent.com/darioizzo/geodesyNets/master/figures/bennu_low.gif)

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