# One flow to correct them all: improving simulations in high-energy physics with a single normalising flow and a switch

arXiv: https://arxiv.org/abs/2403.18582 · HTML: https://mlsanity.com/paper/2403.18582/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 27 Mar 2024.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [Invertible Generative Modeling using Linear Rational Splines](https://mlsanity.com/paper/2001.05168/) (2020)
- [Cubic-Spline Flows](https://mlsanity.com/paper/1906.02145/) (2019)
- [DCTRGAN: Improving the Precision of Generative Models with Reweighting](https://mlsanity.com/paper/2009.03796/) (2020)
- [Neural Networks for Full Phase-space Reweighting and Parameter Tuning](https://mlsanity.com/paper/1907.08209/) (2019)
- [Reweighting with Boosted Decision Trees](https://mlsanity.com/paper/1608.05806/) (2016)
- [Flow Away your Differences: Conditional Normalizing Flows as an Improvement to Reweighting](https://mlsanity.com/paper/2304.14963/) (2023)
- [Transport away your problems: Calibrating stochastic simulations with optimal transport](https://mlsanity.com/paper/2107.08648/) (2021)

## Built on by (most cited first, 4 of 4)

- [Profiling systematic uncertainties in Simulation-Based Inference with Factorizable Normalizing Flows](https://mlsanity.com/paper/2602.13184/) (2026)
- [Factorizable Normalizing Flows for parameter-dependent density morphing](https://mlsanity.com/paper/2606.30489/) (2026)
- [Unknown Unknowns: Model Misspecification in Machine Learning for Physics](https://mlsanity.com/paper/2608.13633/) (2026)
- [Learning Minimal-Deviation Corrections for Multi-Dimensional Mismodelling in HEP Simulations](https://mlsanity.com/paper/2605.07460/) (2026)

## Abstract (arXiv)

Simulated events are key ingredients in almost all high-energy physics analyses. However, imperfections in the simulation can lead to sizeable differences between the observed data and simulated events. The effects of such mismodelling on relevant observables must be corrected either effectively via scale factors, with weights or by modifying the distributions of the observables and their correlations. We introduce a correction method that transforms one multidimensional distribution (simulation) into another one (data) using a simple architecture based on a single normalising flow with a boolean condition. We demonstrate the effectiveness of the method on a physics-inspired toy dataset with non-trivial mismodelling of several observables and their correlations.