Two-scale coupling for preconditioned Hamiltonian Monte Carlo in infinite dimensions

Abstract

We derive non-asymptotic quantitative bounds for convergence to equilibrium of the exact preconditioned Hamiltonian Monte Carlo algorithm (pHMC) on a Hilbert space. As a consequence, explicit and dimension-free bounds for pHMC applied to high-dimensional distributions arising in transition path sampling and path integral molecular dynamics are given. Global convexity of the underlying potential energies is not required. Our results are based on a two-scale coupling which is contractive in a carefully designed distance.

36 pages, 4 figures

References in corpus (3)

• Spectral gaps in Wasserstein distances and the 2D stochastic Navier--Stokes equations
• Cayley modification for strongly stable path-integral and ring-polymer molecular dynamics
• Dimension-free path-integral molecular dynamics without preconditioning

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