Optimal sampling strategies in event-chain Monte Carlo
Abstract
Event-chain Monte Carlo (ECMC) has revolutionised computational sampling over recent years, providing a powerful alternative to the molecular-dynamics (MD) and Hamiltonian Monte Carlo (HMC) algorithms. Each method outperforms the ubiquitous random-walk Metropolis algorithm by advancing particles along deterministic trajectories, but ECMC achieves this without being constrained by Newtonian dynamics. Recent advances exploited this dynamical freedom to induce a collective particle dynamics that relax local density variations on fast timescales. In a foundational model of N pairwise-interacting particles on the 1D torus, this led to an O(N3/4) improvement on the industry-leading computational efficiency of MD and HMC - but with an impractically small prefactor at low/high mean particle density for general attractive/repulsive interactions. Here we present a universal framework that generalises this high-efficiency sampling strategy to all translationally symmetric pairwise models on the torus - creating the potential to surpass MD and HMC as the state of the art. We also numerically elucidate the collective particle dynamics and discuss broad impact across the physical sciences and computational statistics.
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BibTeX
@misc{gulliford2026optimal,
title = {{Optimal sampling strategies in event-chain Monte Carlo}},
author = {James Gulliford and Gareth O. Roberts and Michael F. Faulkner},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01659},
eprint = {2610.01659},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01659},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimal sampling strategies in event-chain Monte Carlo
AU - James Gulliford
AU - Gareth O. Roberts
AU - Michael F. Faulkner
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01659
UR - https://arxiv.org/abs/2610.01659
AB - Event-chain Monte Carlo (ECMC) has revolutionised computational sampling over recent years, providing a powerful alternative to the molecular-dynamics (MD) and Hamiltonian Monte Carlo (HMC) algorithms. Each method outperforms the ubiquitous random-walk Metropolis algorithm by advancing particles along deterministic trajectories, but ECMC achieves this without being constrained by Newtonian dynamics. Recent advances exploited this dynamical freedom to induce a collective particle dynamics that relax local density variations on fast timescales. In a foundational model of N pairwise-interacting particles on the 1D torus, this led to an O(N^3/4) improvement on the industry-leading computational efficiency of MD and HMC - but with an impractically small prefactor at low/high mean particle density for general attractive/repulsive interactions. Here we present a universal framework that generalises this high-efficiency sampling strategy to all translationally symmetric pairwise models on the torus - creating the potential to surpass MD and HMC as the state of the art. We also numerically elucidate the collective particle dynamics and discuss broad impact across the physical sciences and computational statistics.
ER -