SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 4, Page 1446-1492, January 2020.
In this work, we combine a stochastic model reduction with a particle filter augmented with tempering and jittering, and apply the combined algorithm to a damped and forced incompressible two-dimensional Euler dynamics defined on a simply connected bounded domain. We show that using the combined algorithm, we are able to assimilate data from a reference system state (the “truth'') modeled by a highly resolved numerical solution of the flow that has roughly $3.1 \times 10^6$ degrees of freedom, into a stochastic system having two orders of magnitude less degrees of freedom, which is able to approximate the true state reasonably accurately for five large-scale eddy turnover times, using modest computational hardware. The model reduction is performed through the introduction of a stochastic advection by Lie transport (SALT) model as the signal on a coarser resolution. The SALT approach was introduced as a general theory using a geometric mechanics framework from Holm [Proc. A, 471 (2015)]. This work follows on the numerical implementation for SALT presented by Cotter et al. [SIAM Multiscale Model. Simul., 17 (2019), pp. 192--232] for the flow in consideration. The model reduction is substantial: the reduced SALT model has $4.9 \times 10^4$ degrees of freedom. Results from reliability tests on the assimilated system are also presented.

中文翻译：

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李传运用于随机对流的粒子滤波：以阻尼和强迫不可压缩二维欧拉方程为例

SIAM / ASA不确定性量化期刊，第8卷，第4期，第1446-1492页，2020年1月。
在这项工作中，我们将随机模型简化与通过回火和抖动增强的粒子滤波器组合在一起，并将组合算法应用于在简单连接的有界域上定义的阻尼且强制不可压缩的二维欧拉动力学。我们证明，使用组合算法，我们可以从参考系统状态（“真相”）中吸收数据，该状态由具有大约$ 3.1 \乘以10 ^ 6 $自由度的流的高度解析数值解决方案建模，进入具有小于两个数量级的自由度的随机系统，该系统能够使用适度的计算硬件，在五个大规模涡流转换时间内合理准确地逼近真实状态。通过引入随机平流（通过李氏运输（SALT）模型）来进行模型简化，该信号作为较粗分辨率的信号。SALT方法是使用Holm的几何力学框架作为一般理论引入的。A，471（2015）。这项工作遵循了Cotter等人提出的SALT数值实现方法。[SIAM多尺度模型。Simul。，17（2019），pp.192--232]。该模型的减少是巨大的：减少后的SALT模型具有$ 4.9 \乘以10 ^ 4 $的自由度。还介绍了对同化系统进行可靠性测试的结果。这项工作遵循了Cotter等人提出的SALT数值实现方法。[SIAM多尺度模型。Simul。，17（2019），pp.192--232]。该模型的减少是巨大的：减少后的SALT模型具有$ 4.9 \乘以10 ^ 4 $的自由度。还介绍了对同化系统进行可靠性测试的结果。这项工作遵循了Cotter等人提出的SALT数值实现方法。[SIAM多尺度模型。Simul。，17（2019），pp.192--232]。该模型的减少是巨大的：减少后的SALT模型具有$ 4.9 \乘以10 ^ 4 $的自由度。还介绍了对同化系统进行可靠性测试的结果。