## Project

# Micro-macro accelerated Markov chain Monte Carlo methods with applications in molecular dynamics and data assimilation

Computational science has emerged as a ‘third pillar of science’, complementing theory and experiments in disciplines. This evolution is not only due to increased computing power, but also to mathematical advances that led to more efficient computational algorithms. This proposal connects two remaining challenges concerning the modeling and simulation of systems of interacting particles. First, many interacting particle systems exhibit multiscale behavior, with a large time-scale separation between the (fast) dynamics of individual particles and the (slow) evolution of the macroscopic quantities of interest. Second, calibration of these models usually requires assimilating large quantities of experimental data.

For systems of interacting particles, one is often interested in sampling the system’s statistical equilibrium state to compute some macroscopic quantities of interest. Markov chain Monte Carlo methods perform this task via a long time integration. Typical applications are molecular dynamics, where the quantity of interest can be some material property, and data assimilation. We will develop micro-macro acceleration methods that exploit a macroscopic level of description to accelerate Markov chain Monte Carlo sampling. The formulation of these algorithms will give rise to a number of mathematical challenges, in terms of convergence properties and efficiency, which we will study on simplified model problems.