  The complexity of real-world geophysical systems is often compounded by the
fact that the observed measurements depend on hidden variables. These latent
variables include unresolved small scales and/or rapidly evolving processes,
partially observed couplings, or forcings in coupled systems. This is the case
in ocean-atmosphere dynamics, for which unknown interior dynamics can affect
surface observations. The identification of computationally-relevant
representations of such partially-observed and highly nonlinear systems is thus
challenging and often limited to short-term forecast applications. Here, we
investigate the physics-constrained learning of implicit dynamical embeddings,
leveraging neural ordinary differential equation (NODE) representations. A key
objective is to constrain their boundedness, which promotes the generalization
of the learned dynamics to arbitrary initial condition. The proposed
architecture is implemented within a deep learning framework, and its relevance
is demonstrated with respect to state-of-the-art schemes for different
case-studies representative of geophysical dynamics.
