用强化学习动态调整多尺度天体模拟的耦合步长,兼顾精度与效率。
ReLaTS: a Reinforcement Learning-based method for dynamically determining the coupling Time Step in multi-scale simulations of self-gravitating systems

- 基于强化学习自动选择耦合时间步,无需人工调参。
- 相比固定步长方法,显著降低能量误差,且计算开销几乎不变。
- 适用于不同规模星团与行星系统,泛化性强,适合天文模拟新手使用。
天体物理模拟常通过子系统分解、定制积分方案和固定人工设定的时间尺度进行多尺度、多物理问题求解。本文提出ReLaTS,一种基于强化学习的框架,可动态选择耦合时间步,以优化精度与计算成本之间的权衡。我们在含行星系统的星团中验证该方法,通过改变恒星数$N_ ext{star}$和围绕其中一颗恒星运行的行星数$N_{\rm planet}$进行测试。结果表明,该方法能在无需专家知识的情况下找到最优耦合时间步,实现速度与精度的平衡。训练后的网络独立于所耦合的 extit{N}-体算法,在多种设置下均表现稳定。然而,对于质量极小的天体(其总能量贡献远小于大质量体),因网络难以识别积分误差,可靠性下降;在长时间、大规模$N$系统模拟中,误差会累积。尽管如此,强化学习算法仍能将能量误差控制在预设阈值以下。该方法相比固定步长基线显著降低能量误差,且额外计算开销可忽略不计。一旦训练完成,ReLaTS无需专家调优,并具备跨多样天体物理场景的泛化能力,支持自适应多尺度模拟。
原文摘要 · Abstract (English)
Astrophysical simulations frequently address multi-scale, multi-physics problems through subsystem decomposition, problem-tailored integration schemes, and coupling on fixed manually set timescales. Here we introduce ReLaTS, a reinforcement learning framework that dynamically selects the coupling time step to optimize the trade-off between accuracy and computational cost. We validate ReLaTS on star clusters containing a planetary system, and test the method by varying the number of stars $N_\star$ in the cluster and the number of planets ($N_{\rm planet}$) orbiting one of them. The method finds the optimal coupling time step that balances speed and accuracy without requiring expert knowledge. In addition, the trained network operates independently of the coupled \textit{N}-body algorithms, displaying stable performance across a range of setups. We observe that the method is less reliable for cases with infinitesimal masses, as their contribution to the total energy is negligible compared to that of the massive bodies, and the network is not capable of recognizing potential errors generated while integrating them. For long-time integration of large $N$ systems, the error accumulates. The reinforcement learning algorithm, however, manages to keep the energy error below a pre-set threshold. This approach substantially reduces energy errors relative to fixed-time step baselines without substantial additional computational overhead. Once trained, ReLaTS requires no expert tuning and generalizes across diverse astrophysical domains, enabling adaptive multi-scale simulations.
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