Mean Field Limit

The mean field limit describes the behavior of large systems of interacting particles by approximating their collective dynamics with a deterministic equation governing the evolution of the particles' probability distribution. Current research focuses on applying this framework to diverse areas, including neural networks (analyzing training dynamics via stochastic gradient descent and Langevin dynamics), statistical learning (investigating kernel methods and support vector machines in high-dimensional settings), and trajectory inference (recovering population dynamics from snapshots). These studies provide rigorous mathematical foundations for understanding complex systems and offer improved algorithms for machine learning and data analysis, leading to more efficient and accurate solutions in various applications.