Temperature and Friction Accelerated Sampling of Boltzmann-Gibbs Distribution

TL;DR

This paper investigates how tuning friction and temperature in Langevin dynamics can accelerate sampling from the Boltzmann-Gibbs distribution, analyzing optimal parameters and cooling schedules for efficient convergence.

Contribution

It introduces a method for selecting friction to optimize sampling speed by approximating the Hamiltonian as a critical damped oscillator.

Findings

Near-optimal acceleration achieved with critical damping

Over-heating and cooling strategies improve sampling efficiency

Performance depends on cooling schedule and total simulation time

Abstract

This paper is concerned with tuning friction and temperature in Langevin dynamics for fast sampling from the canonical ensemble. We show that near-optimal acceleration is achieved by choosing friction so that the local quadratic approximation of the Hamiltonian is a critical damped oscillator. The system is also over-heated and cooled down to its final temperature. The performances of different cooling schedules are analyzed as functions of total simulation time.