[Paper Review] Geodesy of irregular small bodies via neural density fields: geodesyNets

Dario Izzo, Pablo Gómez|arXiv (Cornell University)|May 27, 2021

Astro and Planetary Science41 references4 citations

TL;DR

This paper introduces geodesyNets, a neural network-based method that models the 3D density distribution of irregular small bodies using minimal prior knowledge. It achieves sub-1% relative error in gravitational acceleration prediction, even near surfaces, and can reconstruct both shape and internal structure without requiring a pre-existing shape model.

ABSTRACT

We present a novel approach based on artificial neural networks, so-called geodesyNets, and present compelling evidence of their ability to serve as accurate geodetic models of highly irregular bodies using minimal prior information on the body. The approach does not rely on the body shape information but, if available, can harness it. GeodesyNets learn a three-dimensional, differentiable, function representing the body density, which we call neural density field. The body shape, as well as other geodetic properties, can easily be recovered. We investigate six different shapes including the bodies 101955 Bennu, 67P Churyumov-Gerasimenko, 433 Eros and 25143 Itokawa for which shape models developed during close proximity surveys are available. Both heterogeneous and homogeneous mass distributions are considered. The gravitational acceleration computed from the trained geodesyNets models, as well as the inferred body shape, show great accuracy in all cases with a relative error on the predicted acceleration smaller than 1\% even close to the asteroid surface. When the body shape information is available, geodesyNets can seamlessly exploit it and be trained to represent a high-fidelity neural density field able to give insights into the internal structure of the body. This work introduces a new unexplored approach to geodesy, adding a powerful tool to consolidated ones based on spherical harmonics, mascon models and polyhedral gravity.

Motivation & Objective

• Address the challenge of inferring internal mass distribution and shape from gravity measurements for irregular small bodies like asteroids and comets.
• Overcome limitations of traditional gravity models—such as spherical harmonics, mascon, and polyhedral models—that require strong assumptions about shape or density.
• Develop a generic, differentiable, and computationally efficient method for geodesy that does not rely on prior knowledge of body shape.
• Enable high-fidelity reconstruction of both surface shape and internal density structure when shape information is available.
• Demonstrate the method's robustness across diverse bodies, including real asteroids (Bennu, Eros, Itokawa, 67P) and synthetic models (Planetesimal, Torus)

Proposed method

• Train a deep neural network to learn a continuous, differentiable 3D density field (neural density field) within a cubic volume enclosing the body, using gravity measurements as supervision.
• Use a multi-layer perceptron (MLP) with positional encoding to represent the 3D spatial coordinates and predict local density values.
• Train the network using a loss function based on mean absolute error (MAE) between predicted and ground-truth gravitational accelerations, with the latter derived from high-fidelity polyhedral or mascon models.
• Incorporate shape information as an auxiliary input when available, allowing the network to learn more accurate density distributions and improve reconstruction fidelity.
• Standardize all bodies into non-dimensional units (length, mass, time) with G=1, L=1, and M=1, and rescale models so that the maximum coordinate magnitude is δ_max=0.8 within a unit cube.
• Generate synthetic datasets including Planetesimal (from N-body simulations) and Torus (a toroidal shape), both matched to Churyumov–Gerasimenko’s mass and size for consistency

Experimental results

Research questions

• RQ1 Can a neural network learn an accurate, differentiable 3D representation of the internal density distribution of irregular small bodies from gravity data alone, without prior knowledge of the shape?
• RQ2 How accurately can geodesyNets predict gravitational acceleration near the surface of irregular bodies, especially when compared to traditional methods like polyhedral gravity or mascon models?
• RQ3 To what extent can the method recover the true body shape and internal structure when shape information is provided during training?
• RQ4 How does the method perform on bodies with heterogeneous internal density distributions, such as Bennu with polar density anomalies or Itokawa with a dense head region?
• RQ5 Can the approach generalize across vastly different body morphologies, including real asteroids and synthetic shapes like Planetesimal and Torus?

Key findings

• GeodesyNets achieve a relative error of less than 1% in predicted gravitational acceleration, even in close proximity to the asteroid surface, across all tested bodies including Bennu, Eros, Itokawa, and 67P.
• The method successfully reconstructs the body shape from the learned density field without requiring explicit shape input, demonstrating its capability as a self-consistent geodetic model.
• When shape information is provided, geodesyNets significantly improve accuracy and can resolve internal heterogeneities, such as a 2.0× higher density in the polar regions of Bennu or a 1.6× increase in the head of Itokawa.
• The approach enables high-fidelity modeling of complex internal structures, such as a hollow region in the Planetesimal model, by setting internal mascon masses to zero and renormalizing.
• Training geodesyNets is computationally efficient and scalable, with a unified numerical pipeline applicable to diverse bodies ranging from real asteroids to synthetic shapes.
• The method outperforms traditional approaches in scenarios where shape or density assumptions are uncertain, offering a generic alternative to spherical harmonics, mascon, and polyhedral gravity models.