  Machine learning methods based on statistical principles have proven highly
successful in dealing with a wide variety of data analysis and analytics tasks.
Traditional data models are mostly concerned with independent identically
distributed data. The recent success of end-to-end modelling scheme using deep
neural networks equipped with effective structures such as convolutional layers
or skip connections allows the extension to more sophisticated and structured
practical data, such as natural language, images, videos, etc. On the
application side, vector fields are an extremely useful type of data in
empirical sciences, as well as signal processing, e.g. non-parametric
transformations of 3D point clouds using 3D vector fields, the modelling of the
fluid flow in earth science, and the modelling of physical fields.
  This review article is dedicated to recent computational tools of vector
fields, including vector data representations, predictive model of spatial
data, as well as applications in computer vision, signal processing, and
empirical sciences.
