从星历表中寻找天体间有效相互作用核的机器学习方法
Machine Learning for Discovering Effective Interaction Kernels between Celestial Bodies from Ephemerides
摘要：
建立天体运动基本机制的精确和预测模型激发了理论物理学的基本发展。候选理论试图尽可能忠实地解释观测结果，并预测行星、恒星和其他天体的未来位置。我们使用数据驱动的学习方法，扩展了Lu等人（$2019$）和Zhong等人（$2020$）开发的方法，以获得太阳系中天体运动的稳定和准确的模型。我们的模型是基于集体动力学框架，并从美国宇航局喷气推进实验室的发展星历。通过将太阳系中的主要天体建模为成对相互作用的代理，我们的学习模型生成了非常精确的动力学，不仅保留了轨道的固有几何特性，而且还保留了动力学的高度敏感特征，例如近日点进动率。我们的学习模型可以为观测数据提供统一的解释，特别是在再现火星，水星和月球的近日点岁差方面。此外，我们的模型在所有情况下都优于牛顿的万有引力定律，并且在月球上的表现与爱因斯坦的广义相对论中推导出的爱因斯坦-因菲尔德-霍夫曼方程相似，甚至超过。
英文摘要：
Building accurate and predictive models of the underlying mechanisms of celestial motion has inspired fundamental developments in theoretical physics. Candidate theories seek to explain observations and predict future positions of planets, stars, and other astronomical bodies as faithfully as possible. We use a data-driven learning approach, extending that developed in Lu et al. ($2019$) and extended in Zhong et al. ($2020$), to a derive stable and accurate model for the motion of celestial bodies in our Solar System. Our model is based on a collective dynamics framework, and is learned from the NASA Jet Propulsion Lab's development ephemerides. By modeling the major astronomical bodies in the Solar System as pairwise interacting agents, our learned model generate extremely accurate dynamics that preserve not only intrinsic geometric properties of the orbits, but also highly sensitive features of the dynamics, such as perihelion precession rates. Our learned model can provide a unified explanation to the observation data, especially in terms of reproducing the perihelion precession of Mars, Mercury, and the Moon. Moreover, Our model outperforms Newton's Law of Universal Gravitation in all cases and performs similarly to, and exceeds on the Moon, the Einstein-Infeld-Hoffman equations derived from Einstein's theory of general relativity.
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