深势：从相空间快照恢复引力势
Deep Potential: Recovering the gravitational potential from a snapshot of phase space
摘要：
银河系动力学领域的主要目标之一是恢复引力势场。绘制势能图将使我们能够确定整个银河系中物质（包括重子物质和暗物质）的空间分布。我们提出了一种新的方法来确定的引力场从恒星的相空间位置的快照，仅基于最小的物理假设。我们首先训练一个归一化流上观察到的相空间位置的样本，获得一个光滑的，可微近似的相空间分布函数。使用无碰撞玻尔兹曼方程，我们找到了引力势-由前馈神经网络表示-使该分布函数保持稳定。这种方法比以前的参数方法灵活得多，后者将狭窄的分析模型类拟合到数据中。这是一种很有前途的方法，可以利用即将推出的丰富的恒星运动学数据集来揭示银河系的密度结构。
英文摘要：
One of the major goals of the field of Milky Way dynamics is to recover the gravitational potential field. Mapping the potential would allow us to determine the spatial distribution of matter - both baryonic and dark - throughout the Galaxy. We present a novel method for determining the gravitational field from a snapshot of the phase-space positions of stars, based only on minimal physical assumptions. We first train a normalizing flow on a sample of observed phase-space positions, obtaining a smooth, differentiable approximation of the phase-space distribution function. Using the collisionless Boltzmann equation, we then find the gravitational potential - represented by a feed-forward neural network - that renders this distribution function stationary. This method is far more flexible than previous parametric methods, which fit narrow classes of analytic models to the data. This is a promising approach to uncovering the density structure of the Milky Way, using rich datasets of stellar kinematics that will soon become available.
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