Fisher Rao Gradient Flow

Fisher-Rao gradient flow is a framework for analyzing and designing dynamical systems that evolve probability distributions, aiming to efficiently reach a target distribution. Current research focuses on developing and analyzing algorithms based on this framework, including those employing Gaussian mixtures, interacting particle systems, and kernel methods, to address challenges in sampling, Bayesian inference, and optimization problems. These methods offer advantages in handling multimodal distributions, derivative-free computations, and achieving rapid convergence, impacting fields like machine learning, inverse problems, and game theory. The resulting algorithms show promise for improved efficiency and robustness in various applications.