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Numerical and Statistical Methods for the Coarse-Graining of Many-Particle Stochastic Systems

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, 01003, USA

    Markos A. Katsoulakis & Luc Rey-Bellet

  2. Department of Mathematics, University of Tennessee and Oak Ridge National Laboratory, Knoxville, TN, 37996, USA

    Petr Plecháč

Authors
  1. Markos A. Katsoulakis
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  2. Petr Plecháč
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  3. Luc Rey-Bellet
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Correspondence to Markos A. Katsoulakis.

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Katsoulakis, M.A., Plecháč, P. & Rey-Bellet, L. Numerical and Statistical Methods for the Coarse-Graining of Many-Particle Stochastic Systems. J Sci Comput 37, 43–71 (2008). https://doi.org/10.1007/s10915-008-9216-6

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  • DOI: https://doi.org/10.1007/s10915-008-9216-6

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