  The electronic density of states (DOS) quantifies the distribution of the
energy levels that can be occupied by electrons in a quasiparticle picture, and
is central to modern electronic structure theory. It also underpins the
computation and interpretation of experimentally observable material properties
such as optical absorption and electrical conductivity. We discuss the
challenges inherent in the construction of a machine-learning (ML) framework
aimed at predicting the DOS as a combination of local contributions that depend
in turn on the geometric configuration of neighbours around each atom, using
quasiparticle energy levels from density functional theory as training data. We
present a challenging case study that includes configurations of silicon
spanning a broad set of thermodynamic conditions, ranging from bulk structures
to clusters, and from semiconducting to metallic behavior. We compare different
approaches to represent the DOS, and the accuracy of predicting quantities such
as the Fermi level, the DOS at the Fermi level, or the band energy, either
directly or as a side-product of the evaluation of the DOS. The performance of
the model depends crucially on the smoothening of the DOS, and there is a
tradeoff to be made between the systematic error associated with the
smoothening and the error in the ML model for a specific structure. We
demonstrate the usefulness of this approach by computing the density of states
of a large amorphous silicon sample, for which it would be prohibitively
expensive to compute the DOS by direct electronic structure calculations, and
show how the atom-centred decomposition of the DOS that is obtained through our
model can be used to extract physical insights into the connections between
structural and electronic features.
