流体流动的降阶建模：机器学习，Kolmogorov屏障，闭合建模和分区
Reduced order modeling of fluid flows: Machine learning, Kolmogorov barrier, closure modeling, and partitioning
摘要：
在本文中，我们提出了一个长短期记忆（LSTM）轻推框架，用于利用噪声测量增强流体流动的降阶模型（ROM）。我们建立在这样一个事实，即在实际应用中，有初始条件，边界条件，模型参数和/或现场测量的不确定性。此外，传统的基于Galerkin投影的非线性ROM（GROMs）由于模态截断而遭受不完美性和解的不稳定性，特别是对于Kolmogorov宽度衰减缓慢的对流主导流。在所提出的LSTM-Nudge方法中，我们融合了不完美的GROM和不确定状态估计的组合预测，稀疏欧拉传感器测量，在动态数据同化框架中提供更可靠的预测。我们说明了这个想法与粘性Burgers问题，作为一个基准测试床与二次非线性和拉普拉斯耗散。我们研究了测量噪声和状态估计不确定性对LSTM Nudge行为性能的影响。我们还表明，它可以充分处理不同水平的时间和空间测量稀疏。我们对所提出的模型进行评估的第一步表明，LSTM轻推可以代表新兴数字孪生系统中可行的实时预测工具。
英文摘要：
In this paper, we put forth a long short-term memory (LSTM) nudging framework for the enhancement of reduced order models (ROMs) of fluid flows utilizing noisy measurements. We build on the fact that in a realistic application, there are uncertainties in initial conditions, boundary conditions, model parameters, and/or field measurements. Moreover, conventional nonlinear ROMs based on Galerkin projection (GROMs) suffer from imperfection and solution instabilities due to the modal truncation, especially for advection-dominated flows with slow decay in the Kolmogorov width. In the presented LSTM-Nudge approach, we fuse forecasts from a combination of imperfect GROM and uncertain state estimates, with sparse Eulerian sensor measurements to provide more reliable predictions in a dynamical data assimilation framework. We illustrate the idea with the viscous Burgers problem, as a benchmark test bed with quadratic nonlinearity and Laplacian dissipation. We investigate the effects of measurements noise and state estimate uncertainty on the performance of the LSTM-Nudge behavior. We also demonstrate that it can sufficiently handle different levels of temporal and spatial measurement sparsity. This first step in our assessment of the proposed model shows that the LSTM nudging could represent a viable realtime predictive tool in emerging digital twin systems.
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