Langevin Dynamic

Langevin dynamics, a stochastic process modeling the evolution of a system under the influence of both deterministic forces and random noise, is a powerful tool for sampling from complex probability distributions and solving optimization problems. Current research focuses on improving the efficiency and robustness of Langevin-based algorithms, particularly in high-dimensional spaces, through techniques like preconditioning, splitting integrators, and incorporating generative priors or piecewise deterministic Markov processes. These advancements have significant implications for Bayesian inference, generative modeling, and various applications including image restoration, quantum computing optimization, and solving inverse problems in fields like signal processing and materials science.