  Cyber-physical systems (CPSs) are usually complex and safety-critical; hence,
it is difficult and important to guarantee that the system's requirements,
i.e., specifications, are fulfilled. Simulation-based falsification of CPSs is
a practical testing method that can be used to raise confidence in the
correctness of the system by only requiring that the system under test can be
simulated. As each simulation is typically computationally intensive, an
important step is to reduce the number of simulations needed to falsify a
specification. We study Bayesian optimization (BO), a sample-efficient method
that learns a surrogate model that describes the relationship between the
parametrization of possible input signals and the evaluation of the
specification.
  In this paper, we improve the falsification using BO by; first adopting two
prominent BO methods, one fits local surrogate models, and the other exploits
the user's prior knowledge. Secondly, the formulation of acquisition functions
for falsification is addressed in this paper. Benchmark evaluation shows
significant improvements in using local surrogate models of BO for falsifying
benchmark examples that were previously hard to falsify. Using prior knowledge
in the falsification process is shown to be particularly important when the
simulation budget is limited. For some of the benchmark problems, the choice of
acquisition function clearly affects the number of simulations needed for
successful falsification.
