论文标题
流体流的订单建模减少：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
论文作者
论文摘要
在本文中，我们提出了长期的短期记忆（LSTM）裸框架，以增强利用嘈杂测量值的流体流量减少订单模型（ROM）。我们基于这样一个事实，即在现实的应用中，在初始条件，边界条件，模型参数和/或现场测量中存在不确定性。此外，由于模态截断，基于盖勒金投影（GROM）的常规非线性ROM遭受了不完美和解决方案不稳定性的影响，尤其是对于kolmogorov宽度缓慢而衰变的较慢的衰变。在提出的LSTM-nudge方法中，我们从不完美的GROM和不确定状态估计的组合以及稀疏的Eulerian传感器测量结果中融合了预测，以在动态数据同化框架中提供更可靠的预测。我们用粘性汉堡问题说明了这个想法，这是一个具有二次非线性和拉普拉斯耗散的基准测试床。我们研究了测量噪声和状态估计不确定性对LSTM-nuggh行为性能的影响。我们还证明它可以充分处理不同水平的时间和空间测量稀疏性。我们对提出模型的评估的第一步表明，LSTM轻推可以代表新兴的数字双胞胎系统中可行的实时预测工具。
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.
