  The introduction of relevant physical information into neural network
architectures has become a widely used and successful strategy for improving
their performance. In lattice gauge theories, such information can be
identified with gauge symmetries, which are incorporated into the network
layers of our recently proposed Lattice Gauge Equivariant Convolutional Neural
Networks (L-CNNs). L-CNNs can generalize better to differently sized lattices
than traditional neural networks and are by construction equivariant under
lattice gauge transformations. In these proceedings, we present our progress on
possible applications of L-CNNs to Wilson flow or continuous normalizing flow.
Our methods are based on neural ordinary differential equations which allow us
to modify link configurations in a gauge equivariant manner. For simplicity, we
focus on simple toy models to test these ideas in practice.
