Sampling Using Hybrid Stochastic Dynamics
For researchers in computational statistics and molecular dynamics, this provides a principled method to accelerate sampling in complex energy landscapes.
This work proposes a framework for sampling from Gibbs distributions using hybrid stochastic dynamics that couple two different dynamics across regions, achieving exponential convergence to equilibrium and improved mean exit times in metastable landscapes.
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.