  The existing Neural ODE formulation relies on an explicit knowledge of the
termination time. We extend Neural ODEs to implicitly defined termination
criteria modeled by neural event functions, which can be chained together and
differentiated through. Neural Event ODEs are capable of modeling discrete and
instantaneous changes in a continuous-time system, without prior knowledge of
when these changes should occur or how many such changes should exist. We test
our approach in modeling hybrid discrete- and continuous- systems such as
switching dynamical systems and collision in multi-body systems, and we propose
simulation-based training of point processes with applications in discrete
control.
