Continuous Learning of Gravity Field Irregularities Around Small Bodies via Neural Hamiltonian ODEs

2026-09-10

AI Summary

提出使用神经哈密顿ODE直接从跟踪数据中学习小天体附近未知的动力学，无需加速度或势能标签，通过持续学习方法更新网络。

Abstract

We propose to learn the unknown dynamics in the proximity of a small body directly from tracking data, representing them as a feed-forward neural network embedded in the system Hamiltonian. The equations of motion form a Neural Hamiltonian Ordinary Differential Equation, whose variational equations provide exact training gradients: estimation uses position and velocity arcs at realistic noise levels, without acceleration or potential labels, and a continual learning approach warm-starts the network as new data are acquired. The known part of the Hamiltonian carries whatever is available, from the central term and spin state to the constant-density model of the imaged shape. We assess the method against a normalized spherical harmonics expansion estimated from identical arcs through the same machinery, on scenarios built on the shapes of Itokawa, 67P, Bennu and Eros. The network remains usable inside the Brillouin sphere: it plans ballistic descents at Itokawa to \SI{4.6}{m} median touchdown error from tracking alone, against 5.1--\SI{48.9}{m} for harmonics of degree 4--12, and to \SI{0.9}{m} with the imaged shape as prior, a configuration that also recovers localised density anomalies invisible to any harmonics degree. The two representations are complementary, and we discuss their combined use across the phases of a small-body mission.

Problem

• small body
• dynamics learning
• tracking data
• Hamiltonian
• neural network

Innovation

• Neural Hamiltonian ODEs
• Continual Learning
• Small Body Dynamics
• Gravity Field Irregularities
• Tracking Data