Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltonian
Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltonian
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DOI：
10.48550/arxiv.2210.00090
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发表时间：
2022-09
期刊：
影响因子：
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通讯作者：
Oswin So;Gongjie Li;Evangelos A. Theodorou;Molei Tao
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文献类型：
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作者：
Oswin So;Gongjie Li;Evangelos A. Theodorou;Molei Tao
将物理动力学的哈密顿结构整合到深度学习模型中，为提高可解释性和预测精度提供了一种强有力的方法。虽然以前的工作大多局限于欧几里得空间，但当旋转形成动力学的关键组成部分时，例如n体天体相互作用的高阶物理超越简单的点质量动力学时，需要将其扩展到李群流形。此外，这些过程的多尺度性质对现有方法提出了挑战，因为需要很长的时间范围。通过利用一个辛李群流形保持积分器，我们提出了一种数据驱动的非牛顿天文学发现方法。初步结果表明，这两种性质对训练稳定性和预测精度的重要性。
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.