Multi-level Coarse Grained Monte Carlo methods
Seminar Room 1, Newton Institute
Microscopic systems with complex interactions arise in numerous applications such as micromagnetics, epitaxial growth and polymers. In particular, many-particle, microscopic systems with combined short- and long-range interactions are ubiquitous in science and engineering applications exhibiting rich mesoscopic morphologies. In this work we propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models. We design a Metropolis-type algorithm with proposal probability transition matrix based on the coarse graining approximating measures. The method is capable of handling correctly long and short range interactions while accelerating computational simulations. It is proved theoretically and numerically that the proposed algorithm samples correctly the desired microscopic measure, has comparable mixing properties with the classical microscopic Metropolis algorithm and reduces the computational cost due to coarse-grained representations of the microscopic interactions. We also discuss extensions to Kinetic Monte Carlo algorithms. This is a joint work with E. Kalligianaki (Oak Ridge National Lab, USA) and P. Plechac (University of Tennessee & Oak Ridge National Lab, USA).