Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems
Publication Date
2007
Journal or Book Title
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
Abstract
The primary objective of this work is to develop coarse-graining schemes for stochastic many-body microscopic models and quantify their effectiveness in terms of a priori and a posteriori error analysis. In this paper we focus on stochastic lattice systems of interacting particles at equilibrium. The proposed algorithms are derived from an initial coarse-grained approximation that is directly computable by Monte Carlo simulations, and the corresponding numerical error is calculated using the specific relative entropy between the exact and approximate coarse-grained equilibrium measures. Subsequently we carry out a cluster expansion around this first – and often inadequate – approximation and obtain more accurate coarse-graining schemes. The cluster expansions yield also sharp a posteriori error estimates for the coarse-grained approximations that can be used for the construction of adaptive coarse-graining methods. We present a number of numerical examples that demonstrate that the coarse-graining schemes developed here allow for accurate predictions of critical behavior and hysteresis in systems with intermediate and long-range interactions. We also present examples where they substantially improve predictions of earlier coarse-graining schemes for short-range interactions.
Pages
627-660
Volume
41
Issue
3
Recommended Citation
Katsoulakis, MA; Plechac, P; Rey-Bellet, L; and Tsagkarogiannis, DK, "Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems" (2007). ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE. 775.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/775
Comments
The published version is located at http://www.esaim-m2an.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/m2an/abs/2007/03/m2an0652/m2an0652.html