Stochastic Gradient Langevin Dynamics (SGLD) shows its advantages in multi-modal sampling and non-convex optimization, which implies broad application in machine learning, e.g., uncertainty quantification for AI safety problems, training of neural networks, etc. The core issue in this field concerns the SGLD algorithm’s acceleration and convergence rate of the continuous time (mean-field) Langevin diffusion process to its invariant distribution. In this talk, I will present the general idea of entropy dissipation and show the convergence rate analysis for linear and non-linear Fokker-Planck equations. I will show some applications by using various Langevin dynamics-based algorithms.