Quantitative acceleration of convergence to invariant distribution by irreversibility in diffusion processes

PDE Seminar
Tuesday, December 5, 2023 - 3:30pm for 1 hour (actually 50 minutes)
Skiles 005
Yuqing Wang – Georgia Tech – ywang3398@gatech.edu
Lukas Wessels

Sampling from the Gibbs distribution is a long-standing problem studied across various fields. Among many sampling algorithms, Langevin dynamics plays a crucial role, particularly for high-dimensional target distributions. In practical applications, accelerating sampling dynamics is always desirable. It has long been studied that adding an irreversible component to reversible dynamics, such as Langevin, can accelerate convergence. Concrete constructions of irreversible components have also been explored in specific scenarios. However, a general strategy for such construction is still elusive. In this talk, I will introduce the concept of leveraging irreversibility to accelerate general dynamics, along with the quantification of irreversible dynamics. Our theory is mainly based on designing a modified entropy functional originally developed for linear kinetic equations (Dolbeault et al., 2015).