We consider the problem of embedding point cloud data sampled from an
underlying manifold with an associated flow or velocity. Such data arises in
many contexts where static snapshots of dynamic entities are measured,
including in high-throughput biology such as single-cell transcriptomics.
Existing embedding techniques either do not utilize velocity information or
embed the coordinates and velocities independently, i.e., they either impose
velocities on top of an existing point embedding or embed points within a
prescribed vector field. Here we present FlowArtist, a neural network that
embeds points while jointly learning a vector field around the points. The
combination allows FlowArtist to better separate and visualize
velocity-informed structures. Our results, on toy datasets and single-cell RNA
velocity data, illustrate the value of utilizing coordinate and velocity
information in tandem for embedding and visualizing high-dimensional data.

在这篇研究中，我们介绍了一种名为 FlowArtist 的神经网络，它能够同时学习点云数据的嵌入和点周围的速度场，从而更好地分离和可视化速度相关的结构。通过在嵌入过程中利用坐标和速度信息，FlowArtist 能够有效地嵌入和展示高维度的数据。