  Epidemiological models must be calibrated to ground truth for downstream
tasks such as producing forward projections or running what-if scenarios. The
meaning of calibration changes in case of a stochastic model since output from
such a model is generally described via an ensemble or a distribution. Each
member of the ensemble is usually mapped to a random number seed (explicitly or
implicitly). With the goal of finding not only the input parameter settings but
also the random seeds that are consistent with the ground truth, we propose a
class of Gaussian process (GP) surrogates along with an optimization strategy
based on Thompson sampling. This Trajectory Oriented Optimization (TOO)
approach produces actual trajectories close to the empirical observations
instead of a set of parameter settings where only the mean simulation behavior
matches with the ground truth.
