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MiS Preprint

Mathematical strategies in the coarse-graining of extensive systems: error quantification and adaptivity

Markos Katsoulakis, Petr Plechac, Luc Rey-Bellet and Dimitrios Tsagkarogiannis


In this paper we continue our study of coarse-graining schemes for stochastic many-body microscopic models started in previous work, focusing on equilibrium stochastic lattice systems. Using cluster expansion techniques we expand the exact coarse-grained Hamiltonian around a first approximation and derive higher accuracy schemes by including more terms in the expansion. The accuracy of the coarse-graining schemes is measured in terms of information loss, i.e., relative entropy, between the exact and approximate coarse-grained Gibbs measures. We test the effectiveness of our schemes in systems with competing short and long range interactions, using an analytically solvable model as a computational benchmark. Furthermore, the cluster expansion yields sharp a posteriori error estimates for the coarse-grained approximations that can be computed on-the-fly during the simulation. Based on these estimates we develop a numerical strategy to assess the quality of the coarse-graining and suitably refine or coarsen the simulations. We demonstrate the use of this diagnostic tool in the numerical calculation of phase diagrams.

MSC Codes:
65C05, 65C20, 82B20, 82B80, 82-08
coarse-graining, a posteriori error estimate, adaptive coarse-graining, relative entropy, lattice spin systems, Coarse Grained Monte Carlo method, Gibbs measure, cluster expansion

Related publications

2008 Repository Open Access
Markos A. Katsoulakis, Petr Plechac, Dimitrios K. Tsagkarogiannis and Luc Rey-Bellet

Mathematical strategies in the coarse-graining of extensive systems : error quantification and adaptivity

In: Journal of non-Newtonian fluid mechanics, 152 (2008) 1/3, pp. 101-112