We present AI Poincaré, a machine learning algorithm for autodiscovering conserved quantities using trajectory data from unknown dynamical systems. We test it on five Hamiltonian systems, including the gravitational three-body problem, and find that it discovers not only all exactly conserved quantities, but also periodic orbits, phase transitions, and breakdown timescales for approximate conservation laws.

中文翻译：

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轨迹的机器学习守恒定律

我们介绍了AIPoincaré，这是一种机器学习算法，可使用来自未知动力系统的轨迹数据自动发现守恒量。我们在五个哈密顿系统上对其进行了测试，包括重力三体问题，发现它不仅发现了所有精确守恒的量，而且还发现了近似守恒律的周期轨道，相变和击穿时间尺度。