Lawrence Berkeley National Laboratory Recent Work Title Stochastic Optimal Prediction with Application to Averaged Euler

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. This work was supported in part by the Office of Science, Office of Advanced Scientific Computing Research, Mathematical, Information, and Computational Sciences Division, Applied Mathematical Sciences Subprogram, of the U.S. Department of Energy, under Contract No. DE-AC03-76SF00098, and in part by the National Science Foundation under grant number DMS98-19074. Lawrence Berkeley National Laboratory, Berkeley, CA 94720. Mathematics Department, University of California, Berkeley, CA 94720.

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