  Remote state monitoring over wireless is envisaged to play a pivotal role in
enabling beyond 5G applications ranging from remote drone control to remote
surgery. One key challenge is to identify the system dynamics that is
non-linear with a large dimensional state. To obviate this issue, in this
article we propose to train an autoencoder whose encoder and decoder are split
and stored at a state sensor and its remote observer, respectively. This
autoencoder not only decreases the remote monitoring payload size by reducing
the state representation dimension, but also learns the system dynamics by
lifting it via a Koopman operator, thereby allowing the observer to locally
predict future states after training convergence. Numerical results under a
non-linear cart-pole environment demonstrate that the proposed split learning
of a Koopman autoencoder can locally predict future states, and the prediction
accuracy increases with the representation dimension and transmission power.
