标题： 主动学习遇到分形决策边界：来自Sitnikov三体问题的警示故事 显示英文标题

标题： Active learning meets fractal decision boundaries: a cautionary tale from the Sitnikov three-body problem

摘要： 天文学中到处可见诸如引力N体问题这样的混沌系统。 机器学习（ML）越来越多地被用于预测这些系统的演化，例如为了加速模拟过程。 主动学习（AL）等策略是优化ML训练的自然选择。 在这里，我们展示了在预测Sitnikov三体问题稳定性时主动学习的失败情况，这是展示混沌行为的N体问题的最简单情形。 我们将此失败归因于分类问题决策边界具有分形性质。 这是在恒星团物理、银河动力学或宇宙学背景下通过主动学习优化大量N体模拟的一个潜在陷阱。 显示英文摘要

摘要： Chaotic systems such as the gravitational N-body problem are ubiquitous in astronomy. Machine learning (ML) is increasingly deployed to predict the evolution of such systems, e.g. with the goal of speeding up simulations. Strategies such as active Learning (AL) are a natural choice to optimize ML training. Here we showcase an AL failure when predicting the stability of the Sitnikov three-body problem, the simplest case of N-body problem displaying chaotic behavior. We link this failure to the fractal nature of our classification problem's decision boundary. This is a potential pitfall in optimizing large sets of N-body simulations via AL in the context of star cluster physics, galactic dynamics, or cosmology.