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Numerical and statistical methods for the coarse-graining of many-particle stochastic systems
Journal of Scientific Computing (2008)
  • MA Katsoulakis, University of Massachusetts - Amherst
  • P Plechac
  • L Rey-Bellet, University of Massachusetts - Amherst
In this article we discuss recent work on coarse-graining methods for microscopic stochastic lattice systems. We emphasize the numerical analysis of the schemes, focusing on error quantification as well as on the construction of improved algorithms capable of operating in wider parameter regimes. We also discuss adaptive coarse-graining schemes which have the capacity of automatically adjusting during the simulation if substantial deviations are detected in a suitable error indicator. The methods employed in the development and the analysis of the algorithms rely on a combination of statistical mechanics methods (renormalization and cluster expansions), statistical tools (reconstruction and importance sampling) and PDE-inspired analysis (a posteriori estimates). We also discuss the connections and extensions of our work on lattice systems to the coarse-graining of polymers.
  • coarse-graining,
  • relative entropy,
  • lattice spin systems,
  • polymeric systems,
  • Monte Carlo method,
  • gibbs measure,
  • cluster expansion,
  • multi-body interactions,
  • renormalization group map,
  • adaptivity,
  • a posteriori error analysis,
  • importance sampling
Publication Date
Publisher Statement
DOI: 10.1007/s10915-008-9216-6
Citation Information
MA Katsoulakis, P Plechac and L Rey-Bellet. "Numerical and statistical methods for the coarse-graining of many-particle stochastic systems" Journal of Scientific Computing Vol. 37 Iss. 1 (2008)
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