Equation-free implementation of statistical moment closures

Francis J. Alexander, Gregory Johnson, Gregory L. Eyink, Ioannis G. Kevrekidis

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We present a general numerical scheme for the practical implementation of statistical moment closures suitable for modeling complex, large-scale, nonlinear systems. Building on recently developed equation-free methods, this approach numerically integrates the closure dynamics, the equations of which may not even be available in closed form. Although closure dynamics introduce statistical assumptions of unknown validity, they can have significant computational advantages as they typically have fewer degrees of freedom and may be much less stiff than the original detailed model. The numerical closure approach can in principle be applied to a wide class of nonlinear problems, including strongly coupled systems (either deterministic or stochastic) for which there may be no scale separation. We demonstrate the equation-free approach for implementing entropy-based Eyink-Levermore closures on a nonlinear stochastic partial differential equation.

Original languageEnglish (US)
Article number026701
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number2
StatePublished - Feb 1 2008

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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