  We consider the problem of encoding pairwise correlations between coupled
dynamical systems in a low-dimensional latent space based on few distinct
observations. We used variational autoencoders (VAE) to embed temporal
correlations between coupled nonlinear oscillators that model brain states in
the wake-sleep cycle into a two-dimensional manifold. Training a VAE with
samples generated using two different parameter combinations resulted in an
embedding that represented the whole repertoire of collective dynamics, as well
as the topology of the underlying connectivity network. We first followed this
approach to infer the trajectory of brain states measured from wakefulness to
deep sleep from the two endpoints of this trajectory; next, we showed that the
same architecture was capable of representing the pairwise correlations of
generic Landau-Stuart oscillators coupled by complex network topology
