Neural networks can fit data to learn unknown functions in a process called machine learning. Naturally, as numericists, we want to study this tool in its use for differential equations. Specifically here, we will be interested in non-canonical Hamiltonian problems, i.e. vector fields characterized by a symplectic form (non-canonical) and an invariant energy (Hamiltonian). Such problems include many plasma particle models and planar point vortices. Should the structure be
hard-coded in neural networks? How important is the structure for long-time simulation? What are some differences between continuous and discrete dynamics? These are the questions that will guide this talk.