标题： 用于流体力学中与低分辨率计算技术耦合的数据同化集合卡尔曼滤波器 显示英文标题

标题： Ensemble Kalman Filter for Data Assimilation coupled with low-resolution computations techniques applied in Fluid Dynamics

摘要： 本文提出了一种创新的降阶模型（ROM），通过数据同化（DA）融合实验和仿真数据，以估计流体动力学系统的“真实”状态，从而实现更准确的预测。 我们的方法引入了一种新方法，在降维框架中实施集合卡尔曼滤波器（EnKF），该方法建立在坚实的理论基础之上，并应用于流体动力学。 为了解决数据同化（DA）的大量计算需求，所提出的ROM采用了低分辨率（LR）技术，大幅降低计算成本。 该方法涉及对数据集进行下采样以进行DA计算，随后采用基于低成本奇异值分解（lcSVD）的先进重建技术。 lcSVD方法是本文的一项关键创新，此前从未应用于数据同化（DA），并提供了一种高效的方法，以最小的计算资源提升分辨率。 我们的结果表明，通过LR技术显著减少了计算时间和RAM使用量，而不会影响估计的准确性。 例如，在一个湍流测试案例中，压缩率为15.9的LR方法可以在保持相对均方根误差（RRMSE）为2.6%的情况下，实现13.7倍的速度提升和90.9%的RAM压缩率，相比之下，高分辨率（HR）参考值为0.8%。 此外，我们强调了EnKF在基于有限观测和低保真数值数据估计和预测流体流动系统状态方面的有效性。 本文突出了所提出的DA方法在流体动力学应用中的潜力，特别是在提高计算效率方面，如计算流体力学（CFD）及相关领域。 其在准确性和低计算及内存成本之间取得平衡的能力，使其适用于大规模和实时应用，如环境监测或航空航天。 显示英文摘要

摘要： This paper presents an innovative Reduced-Order Model (ROM) for merging experimental and simulation data using Data Assimilation (DA) to estimate the "True" state of a fluid dynamics system, leading to more accurate predictions. Our methodology introduces a novel approach implementing the Ensemble Kalman Filter (EnKF) within a reduced-dimensional framework, grounded in a robust theoretical foundation and applied to fluid dynamics. To address the substantial computational demands of DA, the proposed ROM employs low-resolution (LR) techniques to drastically reduce computational costs. This approach involves downsampling datasets for DA computations, followed by an advanced reconstruction technique based on low-cost Singular Value Decomposition (lcSVD). The lcSVD method, a key innovation in this paper, has never been applied to DA before and offers a highly efficient way to enhance resolution with minimal computational resources. Our results demonstrate significant reductions in both computation time and RAM usage through the LR techniques without compromising the accuracy of the estimations. For instance, in a turbulent test case, the LR approach with a compression rate of 15.9 can achieve a speed-up of 13.7 and a RAM compression of 90.9% while maintaining a low Relative Root Mean Square Error (RRMSE) of 2.6%, compared to 0.8% in the high-resolution (HR) reference. Furthermore, we highlight the effectiveness of the EnKF in estimating and predicting the state of fluid flow systems based on limited observations and low-fidelity numerical data. This paper highlights the potential of the proposed DA method in fluid dynamics applications, particularly for improving computational efficiency in CFD and related fields. Its ability to balance accuracy with low computational and memory costs makes it suitable for large-scale and real-time applications, such as environmental monitoring or aerospace.