ABSTRACT:

One of the fundamental challenges of accurate simulation of turbulent flows is that initial data is often incomplete, which for said flows is a strong impediment to accurate modeling due to sensitive dependence on initial conditions. Data assimilation is the study of different methods used to adaptively correct models towards the data. These methods can be modified to solve the inverse problem of finding incorrect parameters. Parameter recovery is a popular research area, the methods for which, to the best of the speaker’s knowledge, almost exclusively use data uncertainty as a driving factor in finding such parameters. A continuous data assimilation method, known as the Azouani-Olson-Titi (AOT) or Continuous Data Assimilation (CDA) algorithm, introduced a linear feedback control term to dissipative systems, giving a simple and rigorous deterministic method by which to understand the underpinnings of more complex data assimilation algorithms used in the geosciences for, e.g., weather and climate prediction. A variety of parameter recovery algorithms based on this algorithm have been developed in the last 7 years, opening up a new research area. In this talk, the speaker will present a computational study that is a suite comparison of mixed and matched stochastic and deterministic data assimilation and parameter recovery methods on the multi-scale Lorenz ’96 equations. The results show promising new research directions. This is an upcoming paper (which should be on the arXiv before the speaker gives this talk) with Professor Franca Hoffman (Caltech) and Ashely Wang (Stanford).