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着重要作用，如汽车和航空航天工业、数值天气预报、海洋和环境模拟。然而，计算模型往往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(ROM)的，它是比传统模型复杂度低得多的代理计算模型，但可能会受到保真度较低的影响。提出的研究利用数据同化(DA)框架内的观测数据，融合观测数据和数值数据来开发一种新的稳健的DA-ROM框架。精度是阻碍当前ROM在工业过程中的流体流动、不确定性量化和海洋模拟中大规模应用的根本障碍之一。对几个已解析的只读存储器模式和许多未解析的只读存储器模式之间的相互作用进行建模(即，只读存储器闭包建模)对于只读存储器的准确性至关重要。此外，在开发精确的只读存储器时，还需要吸收现有的物理观测数据，例如来自基本物理系统测量的数据。然而，这种洞察力在今天的只使用数字数据构建的只读存储器中是不存在的。提出的DA-ROM框架利用最先进的DA算法以及观测和数值数据，向真实流体流动的ROM模拟迈进了一大步。构造了两种不同类型的精确只读存储器闭包模型：(A)结构只读存储器闭包模型，其中模型的整个结构是从数据中发现的；(B)近似反卷积只读存储器闭包模型，其中使用图像处理的思想来构建只读存储器，并使用DA来推断参数。此外，来自观测数据和数字数据的信息被融合以构建新的只读存储器闭合模型。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.