  Reachability analysis is a popular method to give safety guarantees for
stochastic cyber-physical systems (SCPSs) that takes in a symbolic description
of the system dynamics and uses set-propagation methods to compute an
overapproximation of the set of reachable states over a bounded time horizon.
In this paper, we investigate the problem of performing reachability analysis
for an SCPS that does not have a symbolic description of the dynamics, but
instead is described using a digital twin model that can be simulated to
generate system trajectories. An important challenge is that the simulator
implicitly models a probability distribution over the set of trajectories of
the SCPS; however, it is typical to have a sim2real gap, i.e., the actual
distribution of the trajectories in a deployment setting may be shifted from
the distribution assumed by the simulator. We thus propose a statistical
reachability analysis technique that, given a user-provided threshold
$1-\epsilon$, provides a set that guarantees that any reachable state during
deployment lies in this set with probability not smaller than this threshold.
Our method is based on three main steps: (1) learning a deterministic surrogate
model from sampled trajectories, (2) conducting reachability analysis over the
surrogate model, and (3) employing {\em robust conformal inference} using an
additional set of sampled trajectories to quantify the surrogate model's
distribution shift with respect to the deployed SCPS. To counter conservatism
in reachable sets, we propose a novel method to train surrogate models that
minimizes a quantile loss term (instead of the usual mean squared loss), and a
new method that provides tighter guarantees using conformal inference using a
normalized surrogate error. We demonstrate the effectiveness of our technique
on various case studies.
