Safe Reach Set Computation via Neural Barrier Certificates

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.