  Neural networks have the ability to serve as universal function
approximators, but they are not interpretable and don't generalize well outside
of their training region. Both of these issues are problematic when trying to
apply standard neural ordinary differential equations (neural ODEs) to
dynamical systems. We introduce the polynomial neural ODE, which is a deep
polynomial neural network inside of the neural ODE framework. We demonstrate
the capability of polynomial neural ODEs to predict outside of the training
region, as well as perform direct symbolic regression without additional tools
such as SINDy.
