  This paper addresses the data-driven identification of latent dynamical
representations of partially-observed systems, i.e., dynamical systems for
which some components are never observed, with an emphasis on forecasting
applications, including long-term asymptotic patterns. Whereas state-of-the-art
data-driven approaches rely on delay embeddings and linear decompositions of
the underlying operators, we introduce a framework based on the data-driven
identification of an augmented state-space model using a neural-network-based
representation. For a given training dataset, it amounts to jointly learn an
ODE (Ordinary Differential Equation) representation in the latent space and
reconstructing latent states. Through numerical experiments, we demonstrate the
relevance of the proposed framework w.r.t. state-of-the-art approaches in terms
of short-term forecasting performance and long-term behaviour. We further
discuss how the proposed framework relates to Koopman operator theory and
Takens' embedding theorem.
