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EclipseNETs: Learning Irregular Small Celestial Body Silhouettes

Giacomo Acciarini, Dario Izzo, Francesco Biscani

TL;DR

This work tackles the challenge of predicting eclipse conditions around irregular small bodies by introducing EclipseNET, a neural-implicit model that reconstructs complex silhouettes with high fidelity and speeds far surpassing traditional ray-tracing. It demonstrates centimeter-level trajectory accuracy and over 100x faster inference by evaluating on Bennu, Itokawa, 67P, and Eros, using Siren-activated networks that outperform ReLU baselines. To address incomplete shape knowledge, the authors integrate NeuralODEs to learn and refine silhouettes directly from trajectory data, yielding a nearly 7x reduction in state error in tested scenarios. The differentiable, online-refinable framework promises real-time applicability for autonomous spacecraft operations and compatibility with modern control and optimization methods.

Abstract

Accurately predicting eclipse events around irregular small bodies is crucial for spacecraft navigation, orbit determination, and spacecraft systems management. This paper introduces a novel approach leveraging neural implicit representations to model eclipse conditions efficiently and reliably. We propose neural network architectures that capture the complex silhouettes of asteroids and comets with high precision. Tested on four well-characterized bodies - Bennu, Itokawa, 67P/Churyumov-Gerasimenko, and Eros - our method achieves accuracy comparable to traditional ray-tracing techniques while offering orders of magnitude faster performance. Additionally, we develop an indirect learning framework that trains these models directly from sparse trajectory data using Neural Ordinary Differential Equations, removing the requirement to have prior knowledge of an accurate shape model. This approach allows for the continuous refinement of eclipse predictions, progressively reducing errors and improving accuracy as new trajectory data is incorporated.

EclipseNETs: Learning Irregular Small Celestial Body Silhouettes

TL;DR

This work tackles the challenge of predicting eclipse conditions around irregular small bodies by introducing EclipseNET, a neural-implicit model that reconstructs complex silhouettes with high fidelity and speeds far surpassing traditional ray-tracing. It demonstrates centimeter-level trajectory accuracy and over 100x faster inference by evaluating on Bennu, Itokawa, 67P, and Eros, using Siren-activated networks that outperform ReLU baselines. To address incomplete shape knowledge, the authors integrate NeuralODEs to learn and refine silhouettes directly from trajectory data, yielding a nearly 7x reduction in state error in tested scenarios. The differentiable, online-refinable framework promises real-time applicability for autonomous spacecraft operations and compatibility with modern control and optimization methods.

Abstract

Accurately predicting eclipse events around irregular small bodies is crucial for spacecraft navigation, orbit determination, and spacecraft systems management. This paper introduces a novel approach leveraging neural implicit representations to model eclipse conditions efficiently and reliably. We propose neural network architectures that capture the complex silhouettes of asteroids and comets with high precision. Tested on four well-characterized bodies - Bennu, Itokawa, 67P/Churyumov-Gerasimenko, and Eros - our method achieves accuracy comparable to traditional ray-tracing techniques while offering orders of magnitude faster performance. Additionally, we develop an indirect learning framework that trains these models directly from sparse trajectory data using Neural Ordinary Differential Equations, removing the requirement to have prior knowledge of an accurate shape model. This approach allows for the continuous refinement of eclipse predictions, progressively reducing errors and improving accuracy as new trajectory data is incorporated.

Paper Structure

This paper contains 8 sections, 10 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Eclipse Function
  4. Irregular Bodies
  5. Spacecraft Dynamics
  6. Learning Small Body Silhouettes with EclipseNET
  7. Learning the Silhouette from Trajectories via NeuralODEs
  8. Conclusions

Figures (5)

  • Figure 1: Schematic illustration of the shadow cast by an irregular body, and its eclipse function $F_\mathcal{B}$.
  • Figure 2: A) 3D models of Bennu, Churyumov-Gerasimenko, Eros, and Itokawa. B) Contour plot of the eclipse function for a fixed viewpoint. C) Sampled points of the eclipse function used to build the training set. D) Eclipse predictions for a Sun direction not included in the training set. The red curve represents an EclipseNet with 2,369 parameters, while the blue curve corresponds to 50,561 parameters.
  • Figure 3: Training loss vs the number of epochs, together with some views of the approximated silhouette for both networks at the first and last epochs, for both Siren and ReLU networks, for the case of 67P/Churyumov–Gerasimenko.
  • Figure 4: left three columns: three different projections of the three-dimensional orbits obtained using EclipseNET as an event; right column: positional coordinate errors between the trajectory computed with EclipseNET as an event and the one obtained using the Möller-Trumbore algorithm.
  • Figure 5: left: orbit around 67P/ Churyumov-Gerasimenko, with eclipse regions highlighted in dark yellow along the trajectory; right: error in the three positional components before (in red) and after (in green) the NeuralODE refinement. Eclipses are here displayed in grey.