Stochastic Optimal Prediction with Application to Averaged Euler Equations
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Stochastic Optimal Prediction with Application to Averaged Euler Equations

  • Author(s): Bell, John
  • Chorin, Alexandre J
  • Crutchfield, William
  • et al.
Abstract

Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is approximated by its conditional expectation with respect to the invariant measure. In higher-order OP, unresolved information is approximated by a stochastic estimator, leading to a system of random or stochastic differential equations. We explain the ideas through a simple example, and then apply them to the solution of Averaged Euler equations in two space dimensions.

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