  Stochastic simulators are an indispensable tool in many branches of science.
Often based on first principles, they deliver a series of samples whose
distribution implicitly defines a probability measure to describe the phenomena
of interest. However, the fidelity of these simulators is not always sufficient
for all scientific purposes, necessitating the construction of ad-hoc
corrections to "calibrate" the simulation and ensure that its output is a
faithful representation of reality. In this paper, we leverage methods from
transportation theory to construct such corrections in a systematic way. We use
a neural network to compute minimal modifications to the individual samples
produced by the simulator such that the resulting distribution becomes properly
calibrated. We illustrate the method and its benefits in the context of
experimental particle physics, where the need for calibrated stochastic
simulators is particularly pronounced.
