  We present a novel technique for online safety verification of autonomous
systems, which performs reachability analysis efficiently for both bounded and
unbounded horizons by employing neural barrier certificates. Our approach uses
barrier certificates given by parameterized neural networks that depend on a
given initial set, unsafe sets, and time horizon. Such networks are trained
efficiently offline using system simulations sampled from regions of the state
space. We then employ a meta-neural network to generalize the barrier
certificates to state space regions that are outside the training set. These
certificates are generated and validated online as sound over-approximations of
the reachable states, thus either ensuring system safety or activating
appropriate alternative actions in unsafe scenarios. We demonstrate our
technique on case studies from linear models to nonlinear control-dependent
models for online autonomous driving scenarios.
