Transforming Reduced-Order Models of Fluids with Data Assimilation

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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.