2000/08/18 by Bell, John, Chorin, Alexandre J., Crutchfield, William
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.math/0008150
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.