  Over the last few years, several works have proposed deep learning
architectures to learn dynamical systems from observation data with no or
little knowledge of the underlying physics. A line of work relies on learning
representations where the dynamics of the underlying phenomenon can be
described by a linear operator, based on the Koopman operator theory. However,
despite being able to provide reliable long-term predictions for some dynamical
systems in ideal situations, the methods proposed so far have limitations, such
as requiring to discretize intrinsically continuous dynamical systems, leading
to data loss, especially when handling incomplete or sparsely sampled data.
Here, we propose a new deep Koopman framework that represents dynamics in an
intrinsically continuous way, leading to better performance on limited training
data, as exemplified on several datasets arising from dynamical systems.
