NeuReach: Learning Reachability Functions from Simulations

We present NeuReach, a tool that uses neural networks for predicting reachable sets from executions of a dynamical system. Unlike existing reachability tools, NeuReach computes a reachability function that outputs an accurate over-approximation of the reachable set for any initial set in a parameterized family. Such reachability functions are useful for online monitoring, verification, and safe planning. NeuReach implements empirical risk minimization for learning reachability functions. We discuss the design rationale behind the optimization problem and establish that the computed output is probably approximately correct. Our experimental evaluations over a variety of systems show promise. NeuReach can learn accurate reachability functions for complex nonlinear systems, including some that are beyond existing methods. From a learned reachability function, arbitrary reachtubes can be computed in milliseconds. NeuReach is available at https://github.com/sundw2014/NeuReach.