ANR Project IPSO
Interacting Particle systems for Sampling and Optimization
Aims of the project: The main objectives of this project are to improve, implement and mathematically analyze sampling and optimisation methods based on interacting particle systems. The work we propose to undertake pertains to two particular classes of methods: consensus-based methods inspired by particle swarm optimisation, and ensemble Kalman-based methods, which were recently revealed to have a close connection to interacting Langevin diffusions. These methods have proven to be successful in variety of applications, including posterior sampling and maximum a posteriori estimation in the context of Bayesian inverse problems, as well as the training of large neural networks.