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We propose a novel Branch-and-Bound method for reachability analysis ofneural networks in both open-loop and closed-loop settings. Our idea is tofirst compute accurate bounds on the Lipschitz constant of the neural networkin certain directions of interest offline using a convex program. We then usethese bounds to obtain an instantaneous but conservative polyhedralapproximation of the reachable set using Lipschitz continuity arguments. Toreduce conservatism, we incorporate our bounding algorithm within a branchingstrategy to decrease the over-approximation error within an arbitrary accuracy.We then extend our method to reachability analysis of control systems withneural network controllers. Finally, to capture the shape of the reachable setsas accurately as possible, we use sample trajectories to inform the directionsof the reachable set over-approximations using Principal Component Analysis(PCA). We evaluate the performance of the proposed method in several open-loopand closed-loop settings.

ReachLipBnB: A branch-and-bound method for reachability analysis of neural autonomous systems using Lipschitz bounds