  Effective control and prediction of dynamical systems often require
appropriate handling of continuous-time and discrete, event-triggered
processes. Stochastic hybrid systems (SHSs), common across engineering domains,
provide a formalism for dynamical systems subject to discrete, possibly
stochastic, state jumps and multi-modal continuous-time flows. Despite the
versatility and importance of SHSs across applications, a general procedure for
the explicit learning of both discrete events and multi-mode continuous
dynamics remains an open problem. This work introduces Neural Hybrid Automata
(NHAs), a recipe for learning SHS dynamics without a priori knowledge on the
number of modes and inter-modal transition dynamics. NHAs provide a systematic
inference method based on normalizing flows, neural differential equations and
self-supervision. We showcase NHAs on several tasks, including mode recovery
and flow learning in systems with stochastic transitions, and end-to-end
learning of hierarchical robot controllers.
