# Applications of flow models to the generation of correlated lattice QCD ensembles

arXiv: https://arxiv.org/abs/2401.10874 · HTML: https://mlsanity.com/paper/2401.10874/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 23 references that are in the map.
- First posted on arXiv 19 Jan 2024.

## Builds on (most cited first, 4 of 4)

- [Aspects of scaling and scalability for flow-based sampling of lattice QCD](https://mlsanity.com/paper/2211.07541/) (2022)
- [Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics](https://mlsanity.com/paper/2309.01156/) (2023)
- [Machine Learning of Thermodynamic Observables in the Presence of Mode Collapse](https://mlsanity.com/paper/2111.11303/) (2021)
- [Training normalizing flows with computationally intensive target probability distributions](https://mlsanity.com/paper/2308.13294/) (2023)

## Built on by (most cited first, 10 of 10)

- [Bayesian RG Flow in Neural Network Field Theories](https://mlsanity.com/paper/2405.17538/) (2024)
- [Practical applications of machine-learned flows on gauge fields](https://mlsanity.com/paper/2404.11674/) (2024)
- [Scaling flow-based approaches for topology sampling in SU(3) gauge theory](https://mlsanity.com/paper/2510.25704/) (2025)
- [Non-Perturbative Trivializing Flows for Lattice Gauge Theories](https://mlsanity.com/paper/2410.13161/) (2024)
- [Generative Models and Statistical Validation](https://mlsanity.com/paper/2605.30453/) (2026)
- [NeuMC -- a package for neural sampling for lattice field theories](https://mlsanity.com/paper/2503.11482/) (2025)
- [A scalable flow-based approach to mitigate topological freezing](https://mlsanity.com/paper/2601.20708/) (2026)
- [A Monte Carlo estimator of flow fields for sampling and noise problems](https://mlsanity.com/paper/2603.00252/) (2026)
- [Machine learning for four-dimensional SU(3) lattice gauge theories](https://mlsanity.com/paper/2604.12416/) (2026)
- [Machine Learning Meets High-Energy Nuclear Physics: From Pattern Recognition to Physics-Integrated Discovery](https://mlsanity.com/paper/2610.12293/) (2026)

## Abstract (arXiv)

Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these correlations can be exploited for variance reduction in the computation of observables. Three different proof-of-concept applications are demonstrated using a novel residual flow architecture: continuum limits of gauge theories, the mass dependence of QCD observables, and hadronic matrix elements based on the Feynman-Hellmann approach. In all three cases, it is shown that statistical uncertainties are significantly reduced when machine-learned flows are incorporated as compared with the same calculations performed with uncorrelated ensembles or direct reweighting.