Friday, December 3, 2021 - 12:00pm to 1:00pm
Event Calendar Category
Uncategorized
Speaker Name
Nisha Chandramoorthy
Affiliation
MIT ACDL
Building and Room number
33-116
Zoom meeting id
91862758072
Join Zoom meeting
https://mit.zoom.us/j/91862758072
Abstract
Data assimilation in high-dimensional chaotic systems is a recurring challenge across disciplines, from meteorology to aerospace engineering. In the Bayesian filtering problem, the posterior distribution of the state of a dynamical system given partial, noisy, past observations is updated recursively. Despite theoretical advances on these Bayesian updates, dynamical information of the underlying chaotic model that can be inferred from simulation data have not been rigorously exploited in Bayesian filtering algorithms. In this talk, we aim to connect the concentration properties of the filtering recursion to observations on the unstable manifold. Further, we explore how this connection can be exploited to speed up numerical approximations of the filtering distributions. Dimension reduction techniques proposed in the fully Bayesian setting parallel the extensive development of rank reduction using the unstable subspace in algorithms based on Kalman updates, such as the extended Kalman filter.