Time-reversal symmetry arises naturally as a structural property in many dynamical systems of interest. While the importance of hard-wiring symmetry is increasingly recognized in machine learning, to date this has eluded time-reversibility. We propose a new neural network architecture for learning time-reversible dynamical systems from data. We focus in particular on an adaptation to symplectic systems, because of their importance in physics-informed learning. (Joint work with Riccardo Valperga (UvA), Kevin Webster, Victoria Klein and Dmitry Turaev (Imperial)).