Discrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics
Discrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics
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DOI：
10.1073/pnas.1512080112
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发表时间：
2015-08-11
影响因子：
11.1
通讯作者：
Lu, Fei
中科院分区：
文献类型：
--
作者：
Chorin, Alexandre J.;Lu, Fei
许多物理系统都是由非线性微分方程描述的，这些方程太复杂而无法完全求解。一种自然的方法是将变量分为直接相关的变量和非直接相关的变量，为更重要的变量制定可解的近似方程，并使用数据和统计方法来解释其他变量的影响。在本文中，我们考虑时间相关的问题，并介绍了一个完全离散的解决方案，这简化了分析的数据和数值算法。由此产生的时间序列识别的NARMAX（非线性自回归移动平均与外源输入）表示熟悉的工程实践。与统计物理的Mori-Zwanzig形式主义的连接进行了讨论，以及应用到Lorenz 96系统。
Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those that are of direct interest and those that are not, formulate solvable approximate equations for the variables of greater interest, and use data and statistical methods to account for the impact of the other variables. In the present paper we consider time-dependent problems and introduce a fully discrete solution method, which simplifies both the analysis of the data and the numerical algorithms. The resulting time series are identified by a NARMAX (nonlinear auto-regression moving average with exogenous input) representation familiar from engineering practice. The connections with the Mori-Zwanzig formalism of statistical physics are discussed, as well as an application to the Lorenz 96 system.