  The molecular dipole moment ($\boldsymbol{\mu}$) is a central quantity in
chemistry. It is essential in predicting infrared and sum-frequency generation
spectra, as well as induction and long-range electrostatic interactions.
Furthermore, it can be extracted directly from high-level quantum mechanical
calculations, making it an ideal target for machine learning (ML). In this
work, we choose to represent this quantity with a physically inspired ML model
that captures two distinct physical effects: local atomic polarization is
captured within the symmetry-adapted Gaussian process regression (SA-GPR)
framework, which assigns a (vector) dipole moment to each atom, while movement
of charge across the entire molecule is captured by assigning a partial
(scalar) charge to each atom. The resulting "MuML" models are fitted together
to reproduce molecular $\boldsymbol{\mu}$ computed using high-level
coupled-cluster theory (CCSD) and density functional theory (DFT) on the QM7b
dataset. The combined model shows excellent transferability when applied to a
showcase dataset of larger and more complex molecules, approaching the accuracy
of DFT at a small fraction of the computational cost. We also demonstrate that
the uncertainty in the predictions can be estimated reliably using a calibrated
committee model. The ultimate performance of the models depends, however, on
the details of the system at hand, with the scalar model being clearly superior
when describing large molecules whose dipole is almost entirely generated by
charge separation. These observations point to the importance of simultaneously
accounting for the local and non-local effects that contribute to
$\boldsymbol{\mu}$; further, they define a challenging task to benchmark future
models, particularly those aimed at the description of condensed phases.
