Transport away your problems: Calibrating stochastic simulations with optimal transport

Abstract

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.

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• Bias and Priors in Machine Learning Calibrations for High Energy Physics
• Reweighting simulated events using machine-learning techniques in the CMS experiment
• Decorrelation using Optimal Transport
• A continuous calibration of the ATLAS flavour-tagging classifiers via optimal transportation maps
• One flow to correct them all: improving simulations in high-energy physics with a single normalising flow and a switch
• Strong CWoLa: Binary Classification Without Background Simulation