Transforming Reduced-Order Models of Fluids with Data Assimilation

计算模型增加了昂贵的物理实验，并在许多现代科学和工程领域发挥重要作用，如汽车和航空航天工业，数值天气预报，海洋和环境建模。然而，计算模型通常需要大量的计算资源，这限制了它们在许多实际应用中的使用。例如，为汽车或飞机设计最佳形状需要使用复杂的计算模型进行大量模拟。这个项目是关于降阶模型（ROMs）的，它是比传统模型复杂性低得多的替代计算模型，但可能会受到保真度较低的影响。该研究利用数据同化（DA）框架内的观测数据，融合观测数据和数值数据，开发出一种新的鲁棒DA- rom框架。准确性是阻碍当前rom在工业过程、不确定性量化和海洋建模中大规模广泛应用的基本障碍之一。对少数已解析的ROM模式和许多未解析的ROM模式之间的相互作用进行建模（即ROM闭包建模）对于ROM精度至关重要。此外，在开发准确的只读存储器时，还需要吸收现有的物理观测，例如来自基础物理系统的测量数据。然而，这种见解在今天的rom中是不可用的，它们只使用数字数据构建。所提出的DA-ROM框架利用最先进的DA算法和观测和数值数据，在现实流体流动的ROM模拟方面取得了重大飞跃。构建了两种不同类型的精确ROM闭包模型：(a)结构化ROM闭包模型，从数据中发现模型的整个结构；(b)近似反卷积ROM闭合模型，其中使用图像处理的思想来构建ROM，并使用DA来推断参数。此外，从观测和数值数据的信息融合，以建立新的ROM关闭模型。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Computational models augment expensive physical experiments and play a significant role in many modern science and engineering fields such as automotive and aerospace industries, numerical weather prediction, and ocean and environmental modeling. However, computational models often require large computational resources, which limits their use in many practical applications. For example, designing an optimal shape for an automobile or an airplane requires a large number of simulations with complex computational models. This project is on reduced order models (ROMs), which are surrogate computational models of much lower complexity than traditional models, but which may suffer from lower fidelity. The proposed research takes advantage of data from observations within a data assimilation (DA) framework and fuses both observational and numerical data to develop a novel robust DA-ROM framework.Accuracy is one of the fundamental barriers that prevent current ROMs from being widely used on a large scale for fluid flows in industrial processes, uncertainty quantification, and ocean modeling. Modeling the interplay between the few resolved ROM modes and the many unresolved ROM modes (i.e., the ROM closure modeling) is critical for ROM accuracy. Furthermore, assimilating available physical observations, for example, data from measurements of the underlying physical system, is also needed in developing accurate ROMs. However, this insight is not available in today’s ROMs, which are constructed using exclusively numerical data. The proposed DA-ROM framework utilizes state-of-the-art DA algorithms and observational and numerical data to take a major leap toward the ROM simulation of realistic fluid flows. Accurate ROM closure models of two different types are constructed: (a) structural ROM closure models, in which the entire structure of the model is discovered from data; and (b) approximate deconvolution ROM closure models, in which ideas from image processing are used to build the ROM, and where the DA is used to infer the parameters. Furthermore, information from both observational and numerical data is fused in order to construct novel ROM closure models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.