Accelerated Sampling of Boltzmann distributions

TL;DR

This paper introduces a simple Hamiltonian modification that significantly accelerates sampling of Boltzmann distributions by reducing relaxation times, especially in systems with high energy barriers, without altering the equilibrium distribution.

Contribution

It presents a novel Hamiltonian modification technique to speed up Boltzmann sampling, demonstrated on a double-well potential.

Findings

Relaxation time is dramatically decreased.

Equilibrium distribution remains unchanged.

Method effective in systems with high energy barriers.

Abstract

The sampling of Boltzmann distributions by stochastic Markov processes, can be strongly limited by the crossing time of high (free) energy barriers. As a result, the system may stay trapped in metastable states, and the relaxation time to the equilibrium Boltzmann distribution may be very large compared to the available computational time. In this paper, we show how, by a simple modification of the Hamiltonian, one can dramatically decrease the relaxation time of the system, while retaining the same equilibrium distribution. The method is illustrated on the case of the one-dimensional double-well potential.