"You Will Be Assimilated: Incorporating Data for Insights into Physics & Mathematics"
Thursday, Mar 21, 2024
Abstract:
One of the challenges of the accurate simulation of turbulent flows is that initial data is often incomplete. Data assimilation circumvents this issue by continually incorporating the observed data into the model. A continuous data assimilation approach known as the Azouani-Olson-Titi (AOT) algorithm introduced a feedback control term to the 2D incompressible Navier-Stokes equations (NSE) in order to incorporate sparse measurements. The solution to the AOT algorithm applied to the 2D NSE was proven to converge exponentially to the true solution of the 2D NSE with respect to the given initial data. In this presentation, we will discuss history of data assimilation for different methods, with an emphasis on the continuous data assimilation algorithm that was used to prove the convergence in the perfect data setting, present various robustness results of the continuous data assimilation algorithm, and discuss how continuous data assimilation can be used to identify and correct model error. We will focus on the implementation of the AOT algorithm in the Model for Prediction Across Scales - Ocean model and present a proof of the convergence of a nonlinear version of the AOT algorithm in the setting of the 2D NSE, where for a portion of time the convergence rate is proven to be double exponential.
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