论文标题
通过学习非欧几里得汉密尔顿的数据驱动的非牛顿天文学发现
Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltonian
论文作者
论文摘要
将汉密尔顿的物理动力结构纳入深度学习模型中，为提高解释性和预测准确性提供了强大的方法。虽然先前的作品大部分仅限于欧几里得空间，但是当旋转构成动力学的关键成分时，需要将其扩展到Lie组歧管，例如，除了简单的点质量动力学以外，用于N体天体相互作用的高级物理学。此外，这些过程的多规则性质对现有方法提出了挑战，因为需要长期的视野。通过利用象征性的lie组歧管保存整合物，我们提出了一种以数据驱动的非牛顿天文学发现的方法。初步结果表明，这两种属性在训练稳定性和预测准确性中的重要性。
Incorporating the Hamiltonian structure of physical dynamics into deep learning models provides a powerful way to improve the interpretability and prediction accuracy. While previous works are mostly limited to the Euclidean spaces, their extension to the Lie group manifold is needed when rotations form a key component of the dynamics, such as the higher-order physics beyond simple point-mass dynamics for N-body celestial interactions. Moreover, the multiscale nature of these processes presents a challenge to existing methods as a long time horizon is required. By leveraging a symplectic Lie-group manifold preserving integrator, we present a method for data-driven discovery of non-Newtonian astronomy. Preliminary results show the importance of both these properties in training stability and prediction accuracy.
