Couplings for Andersen Dynamics
This work addresses a foundational issue in molecular dynamics and MCMC inference, providing theoretical guarantees for convergence in high-dimensional settings, though it appears incremental as it builds on existing dynamics with new coupling techniques.
The paper tackles the problem of understanding convergence to equilibrium for Andersen dynamics, a stochastic process used in molecular simulations and MCMC inference, by presenting couplings that yield sharp convergence bounds in the Wasserstein sense without requiring global convexity of the potential energy.
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.