  Machine learning of scalar molecular properties such as potential energy has
enabled widespread applications. However, there are relatively few machine
learning models targeting directional properties, including permanent and
transition dipole (multipole) moments, as well as polarizability. These
properties are essential to determine intermolecular forces and molecular
spectra. In this chapter, we review machine learning models for these tensorial
properties, with special focus on how to encode the rotational equivariance
into these models by taking a similar form as the physical definition of these
properties. You will then learn how to use an embedded atom neural network
model to train dipole moments and polarizabilities of a representative
molecule. The methodology discussed in this chapter can be extended to learn
similar or higher-rank tensorial properties, such as magnetic dipole moments,
non-adiabatic coupling vectors, and hyperpolarizabilities.
