Optimal prediction with memory
Optimal prediction with memory
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DOI：
10.1016/s0167-2789(02)00446-3
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发表时间：
2002-06-15
影响因子：
4
通讯作者：
Kupferman, R
中科院分区：
文献类型：
--
作者：
Chorin, AJ;Hald, OH;Kupferman, R
最优预测方法估计非线性时间相关问题的解，当解太复杂而无法完全解决或当数据缺失时。解决方案中未解决的组成部分的初始条件是从概率分布中得出的，它们对实际计算的一小组变量的影响通过统计投影进行评估。这种形式类似于不可逆统计力学的投影方法，辅以系统地使用条件期望和求解辅助方程的新方法，即评价非马尔可夫记忆项所需的正交动力学方程。计算结果接近于给定部分数据所能得到的最佳估计。我们详细地介绍了这些结构以及一些有用的变体，提供了简单的例子，并指出了它们与统计物理涨落耗散公式的关系。(C) 2002 Elsevier Science b.v.版权所有
Optimal prediction methods estimate the solution of nonlinear time-dependent problems when that solution is too complex to be fully resolved or when data are missing. The initial conditions for the unresolved components of the solution are drawn from a probability distribution, and their effect on a small set of variables that are actually computed is evaluated via statistical projection. The formalism resembles the projection methods of irreversible statistical mechanics, supplemented by the systematic use of conditional expectations and new methods of solution for an auxiliary equation, the orthogonal dynamics equation, needed to evaluate a non-Markovian memory term. The result of the computations is close to the best possible estimate that can be obtained given the partial data. We present the constructions in detail together with several useful variants, provide simple examples, and point out the relation to the fluctuation-dissipation formulas of statistical physics. (C) 2002 Elsevier Science B.V All rights reserved.