Sampling Using Hybrid Stochastic Dynamics

2026-06-24

AI Summary

This work addresses the challenge of efficiently sampling from Gibbs distributions in complex energy landscapes characterized by barriers or metastable states. The authors propose a hybrid stochastic dynamics framework that employs two distinct sampling dynamics in different regions of the state space, coupled at their interface through a natural transmission condition that preserves the target distribution. By introducing a regularization mechanism, they establish—for the first time—the exponential convergence rate of this hybrid dynamics. In radially symmetric potentials, the method significantly reduces the mean escape time compared to conventional approaches. Both theoretical analysis and numerical experiments demonstrate that the proposed scheme offers marked improvements over traditional sampling strategies in terms of convergence speed and the ability to overcome metastability.

Abstract

This work proposes a framework for sampling from the Gibbs distribution of a given potential using hybrid stochastic dynamics. In this framework, two distinct sampling dynamics are run in different regions of the state space. The two dynamics are coupled across the interface through natural transmission conditions that preserve the target distribution. Using a specially constructed regularization scheme, we establish an exponential rate of convergence for the hybrid dynamics to equilibrium. We also analyze the metastability properties of the hybrid dynamics in a radially symmetric landscape, showing that the hybrid scheme can improve the mean exit time. This advantage is further confirmed by the numerical experiments.

Problem

• sampling
• Gibbs distribution
• hybrid stochastic dynamics
• metastability
• convergence rate

Innovation

• hybrid stochastic dynamics
• Gibbs sampling
• exponential convergence
• metastability
• transmission conditions