Neural network modeling is a key technology of science and research and a platform for deployment of algorithms to systems. In wireless communications, system modeling plays a pivotal role for interference cancellation with specifically high requirements of accuracy regarding the elimination of self-interference in full-duplex relays. This paper hence investigates the potential of identification and representation of the self-interference channel by neural network architectures. The approach is promising for its ability to cope with nonlinear representations, but the variability of channel characteristics is a first obstacle in straightforward application of data-driven neural networks. We therefore propose architectures with a touch of "adaptivity" to accomplish a successful training. For reproducibility of results and further investigations with possibly stronger models and enhanced performance, we document and share our data.