Point classification with Runge-Kutta networks and feature space augmentation

In this paper we combine an approach based on Runge-Kutta Nets considered in [\emph{Benning et al., J. Comput. Dynamics, 9, 2019}] and a technique on augmenting the input space in [\emph{Dupont et al., NeurIPS}, 2019] to obtain network architectures which show a better numerical performance for deep neural networks in point classification problems. The approach is illustrated with several examples implemented in PyTorch.