A mean field approximation in data assimilation for nonlinear dynamics
A mean field approximation in data assimilation for nonlinear dynamics
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DOI：
10.1016/j.physd.2004.04.003
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发表时间：
2004-08-15
影响因子：
4
通讯作者：
Alexander, FJ
中科院分区：
文献类型：
--
作者：
Eyink, GL;Restrepo, JM;Alexander, FJ
本文将资料同化问题转化为非线性随机动力方程组，从最优解由观测条件下的概率提供的观点出发。贝叶斯公式的实现被描述为计算这样的概率。在一个简单的模型与多模态统计的背景下，它表明，条件统计成功地跟踪模式转换，一些标准的次优估计失败。然而，在复杂的模型中，实际上无法计算精确的条件概率。相反，必须寻求条件统计的近似值。在本文中，注意力集中在近似所产生的条件观测数据的分析步骤。一个次优平均场条件分析，从统计力学的时间histolies。它被证明有一个变分公式，减少了近似计算的条件统计的“有效行动”，凸成本函数的最小化。这种平均场分析相比，一个标准的线性分析，基于卡尔曼增益矩阵。在简单模型问题中，平均场条件分析被证明能很好地逼近精确的条件统计量。出版社：Elsevier B.V.
This paper considers the problem of data assimilation into nonlinear stochastic dynamic equations, from the point of view that the optimal solution is provided by the probabilities conditioned upon observations. An implementation of Bayes formula is described to calculate such probabilities. In the context of a simple model with multimodal statistics, it is shown that the conditional statistics succeed in tracking mode transitions where some standard suboptimal estimators fail. However, in complex models the exact conditional probabilities cannot be practically calculated. Instead, approximations to the conditional statistics must be sought. In this paper, attention is focused on approximations to the analysis step arising from the conditioning on observational data. A suboptimal mean-field conditional analysis is obtained from a statistical mechanics of time-histolies. It is shown to have a variational formulation, reducing the approximate calculation of the conditional statistics to the minimization of the "effective action", a convex cost function. This mean-field analysis is compared with a standard linear analysis, based on a Kalman gain matrix. In the simple model problem, the mean-field conditional analysis is shown to approximate well the exact conditional statistics. Pubtished by Elsevier B.V.