标题： 使用归一化流模型去噪银河系恒星巡天数据 显示英文标题

标题： Denoising Milky Way stellar survey data with normalizing flow models

摘要： 盖亚数据集以极高的精度揭示了许多复杂的银河系子结构，包括运动群和相位螺旋。 对这些特征进行精确表征并详细对比理论模型需要处理盖亚的异方差噪声模型，尤其是在银河盘和晕的更远部分。 我们提出了一种通用的、新颖的机器学习方法，使用归一化流进行去噪密度估计，特别关注从恒星巡天数据（如盖亚数据）中的密度估计。 归一化流通过双射变换将一个简单的基础分布转换为复杂的目标分布，从而形成一个高度表达且灵活的模型。 去噪过程使用重要性采样来完成。 我们通过重建被人为添加噪声的局部速度分布，证明了这种方法在盖亚数据上表现优异。例如，我们展示了赫拉克勒斯流的多分支和相空间螺旋都可以被我们的模型很好地捕捉。 我们讨论了超参数的选择以最优恢复子结构，并将我们的方法与极端解卷积进行了比较。 因此，该模型有望成为研究银河系动力学的强大工具，在这些地方盖亚数据的噪声显著。 显示英文摘要

摘要： The Gaia dataset has revealed many intricate Milky Way substructures in exquisite detail, including moving groups and the phase spiral. Precise characterisation of these features and detailed comparisons to theoretical models require engaging with Gaia's heteroscedastic noise model, particularly in more distant parts of the Galactic disc and halo. We propose a general, novel machine-learning approach using normalizing flows for denoising density estimation, with particular focus on density estimation from stellar survey data such as that from Gaia. Normalizing flows transform a simple base distribution into a complex target distribution through bijective transformations resulting in a highly expressive and flexible model. The denoising is performed using importance sampling. We demonstrate that this general procedure works excellently on Gaia data by reconstructing detailed local velocity distributions artificially corrupted with noise. For example, we show the multiple branches of the Hercules stream and the phase-space spiral can both be well captured by our model. We discuss hyperparameter choice to optimally recover substructure and compare our approach to extreme deconvolution. The model therefore promises to be a robust tool for studying the Milky Way's kinematics in Galactic locations where the noise from Gaia is significant.