Speaker. Elisabeth Carlson, Caltech.

Title.  You Will Be Assimilated: Using Data to Accurately Model Fluids with Nonlinear Methods

Abstract. One of the fundamental challenges of accurate simulation of turbulent flows is that initial data is often incomplete, which for turbulent fluid flows is a strong impediment to accurate modeling due to sensitive dependence on initial conditions.  A continuous data assimilation method proposed by Azouani, Olson, and Titi in 2014 introduced a feedback control term to dissipative systems, proving directly how the maximal effectiveness of DA is dependent on the specific physics of the system being investigated.  In this talk, we will focus on the insights of a nonlinear version of the AOT algorithm and distinguish the clear connections to the physics of the existing systems.