# Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems

Markos A. Katsoulakis; Petr Plecháč; Luc Rey-Bellet; Dimitrios K. Tsagkarogiannis

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

- Volume: 41, Issue: 3, page 627-660
- ISSN: 0764-583X

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topKatsoulakis, Markos A., et al. "Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems." ESAIM: Mathematical Modelling and Numerical Analysis 41.3 (2007): 627-660. <http://eudml.org/doc/250071>.

@article{Katsoulakis2007,

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.
},

author = {Katsoulakis, Markos A., Plecháč, Petr, Rey-Bellet, Luc, Tsagkarogiannis, Dimitrios K.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Coarse-graining; a posteriori error estimate; relative entropy;
lattice spin systems; Monte Carlo method; Gibbs measure; cluster expansion;
renormalization group map.; coarse-graining; a posteriori error estimate; lattice spin systems; renormalization group map},

language = {eng},

month = {8},

number = {3},

pages = {627-660},

publisher = {EDP Sciences},

title = {Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems},

url = {http://eudml.org/doc/250071},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Katsoulakis, Markos A.

AU - Plecháč, Petr

AU - Rey-Bellet, Luc

AU - Tsagkarogiannis, Dimitrios K.

TI - Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2007/8//

PB - EDP Sciences

VL - 41

IS - 3

SP - 627

EP - 660

AB -
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.

LA - eng

KW - Coarse-graining; a posteriori error estimate; relative entropy;
lattice spin systems; Monte Carlo method; Gibbs measure; cluster expansion;
renormalization group map.; coarse-graining; a posteriori error estimate; lattice spin systems; renormalization group map

UR - http://eudml.org/doc/250071

ER -

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