Couplings for Andersen Dynamics

Abstract

Andersen dynamics is a standard method for molecular simulations, and a precursor of the Hamiltonian Monte Carlo algorithm used in MCMC inference. The stochastic process corresponding to Andersen dynamics is a PDMP (piecewise deterministic Markov process) that iterates between Hamiltonian flows and velocity randomizations of randomly selected particles. Both from the viewpoint of molecular dynamics and MCMC inference, a basic question is to understand the convergence to equilibrium of this PDMP particularly in high dimension. Here we present couplings to obtain sharp convergence bounds in the Wasserstein sense that do not require global convexity of the underlying potential energy.

36 pages, 8 figures

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Cited by in corpus (4)

• Contraction and Convergence Rates for Discretized Kinetic Langevin Dynamics
• Mixing of Metropolis-Adjusted Markov Chains via Couplings: The High Acceptance Regime
• Unadjusted Hamiltonian MCMC with Stratified Monte Carlo Time Integration
• Randomized Runge-Kutta-Nyström Methods for Unadjusted Hamiltonian and Kinetic Langevin Monte Carlo