Abstract:  Data assimilation is an elegant paradigm for estimating evolving state variable from observations. In the filtering setting, we seek to infer the state distribution conditioned on all the observations available up to that time. Ensemble filtering methods tackle this problem by sequentially updating a set of particles to form an empirical approximation for the filtering distribution. Despite their empirical success, Gaussian filters such as the ensemble Kalman filter (Evensen, J. Geophys. Res., 1994) operate under simplifying assumptions: linearity of the observation model and Gaussianity of the state and observation error. Also it is often assumed that the observations to assimilate are local functions of the state, i.e., that the observations only depend on the state variables that are close by in physical distance. These assumptions are limiting and not representative of many practical settings, thus leading to fundamentally biased inference. Indeed, we often deal with non-Gaussian distributions as well as non-local observations given by integrals of linear and nonlinear functions of the state, such as radiance measured by satellites, fluxes through surfaces, or solutions of elliptic partial differential equations. Leveraging tools from measure transport (Spantini et al., SIAM Review, 2022), we introduce an unifying framework to analyze ensemble filters. Building on the flexibility of this formulation, we present our recent advances to build ensemble filters able to leverage nonlinear, nonlocal, and non-Gaussian features of the filtering problem of interest.

Bio:  Mathieu Le Provost is a Postdoctoral Associate at MIT in the research group of Professor Youssef Marzouk. He received a Ph.D. in Mechanical Engineering from the University of California, Los Angeles under the supervision of Professor Jeff D. Eldredge. He is a recipient of the Dissertation Year Fellowship and the Outstanding Ph.D. Degree Award in Mechanical Engineering from the University of California, Los Angeles. His research interests are in Data Assimilation and Fluid Mechanics. He has a particular interest in exploiting structural properties of forward and inverse problems to develop robust and scalable methods.