# Self-Tuning Hamiltonian Monte Carlo for Accelerated Sampling

arXiv: https://arxiv.org/abs/2309.13593 · HTML: https://mlsanity.com/paper/2309.13593/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 74 references that are in the map.
- First posted on arXiv 24 Sep 2023.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [A Gentle Introduction to Deep Learning for Graphs](https://mlsanity.com/paper/1912.12693/) (2019)
- [TensorFlow Distributions](https://mlsanity.com/paper/1711.10604/) (2017)
- [NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport](https://mlsanity.com/paper/1903.03704/) (2019)
- [TorchMD: A deep learning framework for molecular simulations](https://mlsanity.com/paper/2012.12106/) (2020)
- [Generalizing Hamiltonian Monte Carlo with Neural Networks](https://mlsanity.com/paper/1711.09268/) (2017)
- [A-NICE-MC: Adversarial Training for MCMC](https://mlsanity.com/paper/1706.07561/) (2017)
- [On Sampling with Approximate Transport Maps](https://mlsanity.com/paper/2302.04763/) (2023)

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

- [Uncertainty-biased molecular dynamics for learning uniformly accurate interatomic potentials](https://mlsanity.com/paper/2312.01416/) (2023)
- [Reinforcement Learning for Adaptive MCMC](https://mlsanity.com/paper/2405.13574/) (2024)
- [Fast, Modular, and Differentiable Framework for Machine Learning-Enhanced Molecular Simulations](https://mlsanity.com/paper/2503.20541/) (2025)
- [Harnessing the Power of Reinforcement Learning for Adaptive MCMC](https://mlsanity.com/paper/2507.00671/) (2025)

## Abstract (arXiv)

The performance of Hamiltonian Monte Carlo simulations crucially depends on both the integration timestep and the number of integration steps. We present an adaptive general-purpose framework to automatically tune such parameters, based on a local loss function which promotes the fast exploration of phase-space. We show that a good correspondence between loss and autocorrelation time can be established, allowing for gradient-based optimization using a fully-differentiable set-up. The loss is constructed in such a way that it also allows for gradient-driven learning of a distribution over the number of integration steps. Our approach is demonstrated for the one-dimensional harmonic oscillator and alanine dipeptide, a small protein common as a test case for simulation methods. Through the application to the harmonic oscillator, we highlight the importance of not using a fixed timestep to avoid a rugged loss surface with many local minima, otherwise trapping the optimization. In the case of alanine dipeptide, by tuning the only free parameter of our loss definition, we find a good correspondence between it and the autocorrelation times, resulting in a >100 fold speed up in optimization of simulation parameters compared to a grid-search. For this system, we also extend the integrator to allow for atom-dependent timesteps, providing a further reduction of 25% in autocorrelation times.