# Transport away your problems: Calibrating stochastic simulations with optimal transport

arXiv: https://arxiv.org/abs/2107.08648 · HTML: https://mlsanity.com/paper/2107.08648/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 19 Jul 2021.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [Riemannian Convex Potential Maps](https://mlsanity.com/paper/2106.10272/) (2021)
- [Linearized Optimal Transport for Collider Events](https://mlsanity.com/paper/2008.08604/) (2020)
- [Reweighting with Boosted Decision Trees](https://mlsanity.com/paper/1608.05806/) (2016)

## Built on by (most cited first, 5 of 5)

- [Flow Away your Differences: Conditional Normalizing Flows as an Improvement to Reweighting](https://mlsanity.com/paper/2304.14963/) (2023)
- [One flow to correct them all: improving simulations in high-energy physics with a single normalising flow and a switch](https://mlsanity.com/paper/2403.18582/) (2024)
- [Bias and Priors in Machine Learning Calibrations for High Energy Physics](https://mlsanity.com/paper/2205.05084/) (2022)
- [Unknown Unknowns: Model Misspecification in Machine Learning for Physics](https://mlsanity.com/paper/2608.13633/) (2026)
- [Decorrelation using Optimal Transport](https://mlsanity.com/paper/2307.05187/) (2023)

## Abstract (arXiv)

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.