  In this paper, we present an~algorithm that computes funnels along
trajectories of systems of ordinary differential equations. A funnel is a
time-varying set of states containing the given trajectory, for which the
evolution from within the set at any given time stays in the funnel. Hence it
generalizes the behavior of single trajectories to sets around them, which is
an important task, for example, in robot motion planning.
  In contrast to approaches based on sum-of-squares programming, which poorly
scale to high dimensions, our approach is based on falsification and tackles
the funnel computation task directly, through numerical optimization. This
approach computes accurate funnel estimates far more efficiently and leaves
formal verification to the end, outside all funnel size optimization loops.
