连续学习小天体周围重力场不规则性的神经哈密顿常微分方程
Continuous Learning of Gravity Field Irregularities Around Small Bodies via Neural Hamiltonian ODEs
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中文总结 AI 辅助
提出用神经哈密顿常微分方程从跟踪数据直接学习小天体重力场，持续学习热启动，在Itokawa等场景下优于球谐展开，并可恢复局部密度异常。
中文摘要 AI 辅助
我们提出直接从跟踪数据中学习小天体附近未知动力学的方法，将其表示为嵌入系统哈密顿量中的前馈神经网络。运动方程构成神经哈密顿常微分方程，其变分方程提供精确的训练梯度：估计使用在现实噪声水平下的位置和速度弧段，无需加速度或势标签，并且一种持续学习方法在新数据获取时对网络进行热启动。哈密顿量的已知部分承载所有可用信息，从中心项和自旋状态到成像形状的恒定密度模型。我们针对基于Itokawa、67P、Bennu和Eros形状构建的场景，将该方法与通过相同机制从相同弧段估计的归一化球谐展开进行比较。网络在布里渊球内保持可用：仅通过跟踪数据，在Itokawa上规划弹道下降的中位着陆误差为4.6米，而4至12阶球谐的误差为5.1至48.9米；以成像形状为先验时，误差降至0.9米，这种配置还能恢复任何球谐阶数都无法看到的局部密度异常。这两种表示具有互补性，我们讨论了它们在小天体任务各阶段的联合使用。
英文摘要
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.
发表机构
- European Space Agency（欧洲空间局）
机构由 AI 辅助整理，请以论文原文为准。
