Learning workable representations of dynamical systems is becoming an increasingly important problem in a number of application
areas. By leveraging recent work connecting deep neural networks to systems of differential equations, we propose variational
integrator networks, a class of neural network
architectures designed to preserve the geometric structure of physical systems. This
class of network architectures facilitates accurate long-term prediction, interpretability,
and data-efficient learning, while still remaining highly flexible and capable of modeling
complex behavior. We demonstrate that they
can accurately learn dynamical systems from
both noisy observations in phase space and
from image pixels within which the unknown
dynamics are embedded
