Data assimilation in fluid dynamics

In a (stationary) Bayesian inverse problem, a dimensional reduction can be achieved via a truncated Karhunen-Loeve expansion of the prior distribution. This can significantly reduce the computational complexity in high-dimensional problems. This motivates a similar development for a sequential inverse problem (or sequential data assimilation) of dynamical systems.

Recent advances in the Koopman operator theory provides an efficient tool to compute dominant dynamic modes of a dynamical system from a time-series of data, which enables the construction of a low-dimensional data-driven model. Such a data-driven model is extremely useful for many types of research studies. However, employing it for tracking or predicting the states of a dynamical system in practice can be difficult due to the model error resulting from uncertainty in the training data and the modal truncation.

This research led by Naratip Santitissadeekorn and David Lloyd investigates how a sequential data assimilation tool such as Ensemble Kalman filtering (EnKF) can be combined with the data-driven model to improve prediction skills.