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Improving the prediction of complex nonlinear turbulent dynamical systems using nonlinear filter, smoother and backward sampling techniques
Research in the Mathematical Sciences ( IF 1.2 ) Pub Date : 2020-07-09 , DOI: 10.1007/s40687-020-00216-5
Nan Chen

Predicting complex nonlinear turbulent dynamical systems using partial observations is an important topic. Despite the simplicity of the forecast based on the ensemble mean time series, several critical shortcomings in the ensemble mean forecast and using path-wise measurements to quantify the prediction error are illustrated in this article. Then, a new ensemble method is developed for improving the long-range forecast. This new approach utilizes a mixture of the posterior distributions from data assimilation and is more skillful in predicting non-Gaussian statistics and extreme events than the traditional method by simply running the forecast model forward. Next, a systematic framework of improving forecast models is established, aiming at advancing the predictions at all ranges. The starting model in this new framework belongs to a rich class of nonlinear systems with conditional Gaussian structures. These models allow an efficient nonlinear smoother for state estimation using partial observations, which in turn facilitates a rapid parameter estimation based on an expectation–maximization algorithm. Conditioned on the partially observed time series, the nonlinear smoother further advances an efficient backward sampling of the hidden trajectories, the dynamical and statistical characteristics from which allow a systematic quantification of model error through information theory. The sampled trajectories then serve as the recovered observations of the hidden variables that promote the use of general nonlinear data-driven modeling techniques for a further improvement of the forecast model. A low-order model of the layered topographic equations with regime switching and rare events is used as a test example to illustrate this framework.

中文翻译:

使用非线性滤波器,更平滑和向后采样技术改进对复杂非线性湍流动力系统的预测

利用局部观测预测复杂的非线性湍流动力学系统是一个重要的课题。尽管基于集合平均时间序列的预测很简单,但在本文中仍说明了集合平均预测中的一些关键缺陷,并使用了基于路径的度量来量化预测误差。然后,开发了一种新的集成方法来改善远程预测。这种新方法利用了来自数据同化的后验分布的混合,并且比传统方法通过简单地向前运行预测模型,在预测非高斯统计量和极端事件方面更加熟练。接下来,建立了改进预测模型的系统框架,旨在推进所有范围的预测。这个新框架中的起始模型属于具有条件高斯结构的一类丰富的非线性系统。这些模型允许使用局部观测进行状态估计的高效非线性平滑器,从而有助于基于期望最大化算法的快速参数估计。在部分观测到的时间序列的条件下,非线性平滑器进一步提高了对隐藏轨迹的动态向后采样的能力,这些轨迹的动力学和统计特性可以通过信息论对系统误差进行系统地量化。然后,采样的轨迹充当对隐藏变量的恢复观察,这促进了通用非线性数据驱动的建模技术的使用,从而进一步改善了预测模型。
更新日期:2020-07-09
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