Couplings for Andersen Dynamics

TL;DR

This paper develops coupling methods to analyze the convergence of Andersen dynamics, a stochastic process used in molecular simulations and MCMC, providing sharp bounds without requiring global convexity.

Contribution

It introduces novel coupling techniques to establish convergence bounds for Andersen dynamics, applicable even in non-convex potential energy landscapes.

Findings

Sharp Wasserstein convergence bounds derived

Convergence results hold without global convexity assumptions

Applicable to high-dimensional molecular simulation models

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.