The use of methods resembling (interacting) particle systems has gained a lot of interest for different tasks in machine learning, inverse problems, and related fields.
Popular examples are Langevin-type sampling methods that can be constructed for efficient posterior sampling in Bayesian inverse problems and score-based diffusion models, or consensus type methods that are found in optimization, sampling as well as modern transformer architectures.
In this talk we give an overview of different approaches of recent interest and relate their mathematical analysis to well-known and some novel concepts in statistical mechanics, PDEs, and stochastic processes.
Based on joint works with Lorenz Kuger, Lukas Weigand, Franca Hoffmann, Matthias Erbar, Daniel Matthes, André Schlichting, Tim Roith.