Resonances in reflective Hamiltonian Monte Carlo

Namu Kroupa; Gábor Csányi; Will Handley

doi:10.1103/physreve.111.045308

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arXiv · 2504.12374

Resonances in reflective Hamiltonian Monte Carlo

Namu Kroupa·Gábor Csányi·Will Handley

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Abstract

In high dimensions, reflective Hamiltonian Monte Carlo with inexact reflections exhibits slow mixing when the particle ensemble is initialised from a Dirac delta distribution and the uniform distribution is targeted. By quantifying the instantaneous non-uniformity of the distribution with the Sinkhorn divergence, we elucidate the principal mechanisms underlying the mixing problems. In spheres and cubes, we show that the collective motion transitions between fluid-like and discretisation-dominated behaviour, with the critical step size scaling as a power law in the dimension. In both regimes, the particles can spontaneously unmix, leading to resonances in the particle density and the aforementioned problems. Additionally, low-dimensional toy models of the dynamics are constructed which reproduce the dominant features of the high-dimensional problem. Finally, the dynamics is contrasted with the exact Hamiltonian particle flow and tuning practices are discussed.

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Namu Kroupa, Gábor Csányi, Will Handley. 2025-04-16. Resonances in reflective Hamiltonian Monte Carlo. https://doi.org/10.1103/physreve.111.045308

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