Stochastic Optimal Prediction with Application to Averaged Euler Equations
数值分析
2025-10-20 v1 数值分析
摘要
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.
引用
@article{arxiv.math/0008150,
title = {Stochastic Optimal Prediction with Application to Averaged Euler Equations},
author = {John Bell and Alexandre J. Chorin and William Crutchfield},
journal= {arXiv preprint arXiv:math/0008150},
year = {2025}
}
备注
13 pages, 2 figures