Transport away your problems: Calibrating stochastic simulations with optimal transport

TL;DR

This paper introduces a systematic method using optimal transport and neural networks to calibrate stochastic simulators, improving their fidelity in scientific applications like particle physics.

Contribution

It presents a novel approach combining transportation theory and neural networks to calibrate stochastic simulation outputs effectively.

Findings

Method successfully calibrates simulated distributions to real data.

Application to particle physics demonstrates improved simulation accuracy.

Neural network-based corrections are computationally efficient.

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.