# HMC with Normalizing Flows

arXiv: https://arxiv.org/abs/2112.01586 · HTML: https://mlsanity.com/paper/2112.01586/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 12 references that are in the map.
- First posted on arXiv 2 Dec 2021.

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

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)

## Built on by (most cited first, 6 of 6)

- [Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics](https://mlsanity.com/paper/2309.01156/) (2023)
- [Applications of Machine Learning to Lattice Quantum Field Theory](https://mlsanity.com/paper/2202.05838/) (2022)
- [Practical applications of machine-learned flows on gauge fields](https://mlsanity.com/paper/2404.11674/) (2024)
- [Comparison of Affine and Rational Quadratic Spline Coupling and Autoregressive Flows through Robust Statistical Tests](https://mlsanity.com/paper/2302.12024/) (2023)
- [The NFLikelihood: an unsupervised DNNLikelihood from Normalizing Flows](https://mlsanity.com/paper/2309.09743/) (2023)
- [Neural Surrogate HMC: On Using Neural Likelihoods for Hamiltonian Monte Carlo in Simulation-Based Inference](https://mlsanity.com/paper/2407.20432/) (2024)

## Abstract (arXiv)

We propose using Normalizing Flows as a trainable kernel within the molecular dynamics update of Hamiltonian Monte Carlo (HMC). By learning (invertible) transformations that simplify our dynamics, we can outperform traditional methods at generating independent configurations. We show that, using a carefully constructed network architecture, our approach can be easily scaled to large lattice volumes with minimal retraining effort. The source code for our implementation is publicly available online at https://github.com/nftqcd/fthmc.