Transport away your problems: Calibrating stochastic simulations with optimal transport
It addresses the need for accurate simulations in scientific fields like particle physics, but appears incremental as it applies existing methods to a specific calibration task.
The paper tackles the problem of calibrating stochastic simulators to improve their fidelity by using optimal transport and neural networks to modify samples, demonstrating benefits in experimental particle physics.
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.