  Conventional artificial neural networks are powerful tools in science and
industry, but they can fail when applied to nonlinear systems where order and
chaos coexist. We use neural networks that incorporate the structures and
symmetries of Hamiltonian dynamics to predict phase space trajectories even as
nonlinear systems transition from order to chaos. We demonstrate Hamiltonian
neural networks on the canonical Henon-Heiles system, which models diverse
dynamics from astrophysics to chemistry. The power of the technique and the
ubiquity of chaos suggest widespread utility.
